Sequence Database

A database with 497817 machine generated integer and decimal sequences.

Displaying the first 100 results.

Sequence 2q1rtmulmg2m

1, 1, 2, 2, 4, 2, 6, 4, 6, 4, 10, 4, 12, 6, 8, 8, 16, 6, 18, 8, 12, 10, 22, 8, 20, 12, 18, 12, 28, 8, 30, 16, 20, 16, 24, 12, 36, 18, 24, 16, 40, 12, 42, 20, 24, 22, 46, 16, 42, 20, more...

integer, non-constant, non-monotonic, +, A000010

a(n)=ϕ(n)
ϕ(n)=Euler's totient function
n≥1
2 operations
Prime

Sequence fuae1h3b5z4np

-1, -1, -2, -2, -4, -2, -6, -4, -6, -4, -10, -4, -12, -6, -8, -8, -16, -6, -18, -8, -12, -10, -22, -8, -20, -12, -18, -12, -28, -8, -30, -16, -20, -16, -24, -12, -36, -18, -24, -16, -40, -12, -42, -20, -24, -22, -46, -16, -42, -20, more...

integer, non-constant, non-monotonic, -

a(n)=-ϕ(n)
ϕ(n)=Euler's totient function
n≥1
3 operations
Prime
nϕ~

Sequence ng3ifz13fcfsp

0, 0, 0.6931471806, 0.6931471806, 0.6931471806, 0.6931471806, 0, 0.6931471806, 0, 0.6931471806, 0, 0.6931471806, 0, 0, 0.6931471806, 0.6931471806, 0.6931471806, 0, 0, 0.6931471806, 0, 0, 0, 0.6931471806, 0, 0, 0, 0, 0, 0.6931471806, 0, 0.6931471806, 0, 0.6931471806, 0, 0, 0, 0, 0, 0.6931471806, 0, 0, 0, 0, 0, 0, 0, 0.6931471806, 0, 0, more...

decimal, non-constant, non-monotonic, +0

a(n)=Λ(ϕ(n))
ϕ(n)=Euler's totient function
Λ(n)=Von Mangoldt's function
n≥1
3 operations
Prime
nϕΛ

Sequence t3c44fow4pxrd

0, 0, 0.6931471806, 0.6931471806, 1.3862943611, 0.6931471806, 1.7917594692, 1.3862943611, 1.7917594692, 1.3862943611, 2.302585093, 1.3862943611, 2.4849066498, 1.7917594692, 2.0794415417, 2.0794415417, 2.7725887222, 1.7917594692, 2.8903717579, 2.0794415417, 2.4849066498, 2.302585093, 3.0910424534, 2.0794415417, 2.9957322736, 2.4849066498, 2.8903717579, 2.4849066498, 3.3322045102, 2.0794415417, 3.4011973817, 2.7725887222, 2.9957322736, 2.7725887222, 3.1780538303, 2.4849066498, 3.5835189385, 2.8903717579, 3.1780538303, 2.7725887222, 3.6888794541, 2.4849066498, 3.7376696183, 2.9957322736, 3.1780538303, 3.0910424534, 3.8286413965, 2.7725887222, 3.7376696183, 2.9957322736, more...

decimal, non-constant, non-monotonic, +0

a(n)=ln(ϕ(n))
ϕ(n)=Euler's totient function
n≥1
3 operations
Prime
nϕl

Sequence kqhawrntvxs0k

0, 0, 1, 1, 2, 1, 2, 2, 2, 2, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 3, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 4, 4, 3, 4, 3, 4, 4, 4, 3, 3, 3, 4, 2, 2, 4, 3, 3, more...

integer, non-constant, non-monotonic, +0

a(n)=Ω(ϕ(n))
ϕ(n)=Euler's totient function
Ω(n)=max factorization terms
n≥1
3 operations
Prime
nϕΩ

Sequence egb3cuxm3oa2g

0, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 2, 2, 1, 2, 1, 4, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 2, 1, 1, 4, 1, 2, more...

integer, non-constant, non-monotonic, +0

a(n)=ϕ(Ω(n))
Ω(n)=max factorization terms
ϕ(n)=Euler's totient function
n≥1
3 operations
Prime
nΩϕ

Sequence hleub3fbixhuc

0, 2, 3, 5, 11, 31, 127, 709, 5381, 52711, more...

integer, non-constant, strictly-monotonic, +0

a(n)=p(ϕ(a(n-1)))
a(0)=0
ϕ(n)=Euler's totient function
p(n)=nth prime
n≥0
3 operations
PrimeRecursive
rϕp

Sequence bnhodycfjob1e

0.5403023059, 0.5403023059, -0.4161468365, -0.4161468365, -0.6536436209, -0.4161468365, 0.9601702867, -0.6536436209, 0.9601702867, -0.6536436209, -0.8390715291, -0.6536436209, 0.8438539587, 0.9601702867, -0.1455000338, -0.1455000338, -0.9576594803, 0.9601702867, 0.6603167082, -0.1455000338, 0.8438539587, -0.8390715291, -0.9999608264, -0.1455000338, 0.4080820618, 0.8438539587, 0.6603167082, 0.8438539587, -0.9626058663, -0.1455000338, 0.1542514499, -0.9576594803, 0.4080820618, -0.9576594803, 0.4241790073, 0.8438539587, -0.1279636896, 0.6603167082, 0.4241790073, -0.9576594803, -0.6669380617, 0.8438539587, -0.399985315, 0.4080820618, 0.4241790073, -0.9999608264, -0.4321779449, -0.9576594803, -0.399985315, 0.4080820618, more...

decimal, non-constant, non-monotonic, +-

a(n)=cos(ϕ(n))
ϕ(n)=Euler's totient function
n≥1
3 operations
Prime
nϕO

Sequence k1kebikmym5tj

0.8414709848, 0.8414709848, 0.9092974268, 0.9092974268, -0.7568024953, 0.9092974268, -0.2794154982, -0.7568024953, -0.2794154982, -0.7568024953, -0.5440211109, -0.7568024953, -0.536572918, -0.2794154982, 0.9893582466, 0.9893582466, -0.2879033167, -0.2794154982, -0.7509872468, 0.9893582466, -0.536572918, -0.5440211109, -0.0088513093, 0.9893582466, 0.9129452507, -0.536572918, -0.7509872468, -0.536572918, 0.2709057883, 0.9893582466, -0.9880316241, -0.2879033167, 0.9129452507, -0.2879033167, -0.905578362, -0.536572918, -0.9917788534, -0.7509872468, -0.905578362, -0.2879033167, 0.7451131605, -0.536572918, -0.9165215479, 0.9129452507, -0.905578362, -0.0088513093, 0.9017883476, -0.2879033167, -0.9165215479, 0.9129452507, more...

decimal, non-constant, non-monotonic, +-

a(n)=sin(ϕ(n))
ϕ(n)=Euler's totient function
n≥1
3 operations
Prime
nϕS

Sequence y54gg5hplvokk

1, 1, -1, -1, 0, -1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1, 1, 0, -1, 0, more...

integer, non-constant, non-monotonic, +-0

a(n)=μ(ϕ(n))
ϕ(n)=Euler's totient function
μ(n)=Möbius function
n≥1
3 operations
Prime
nϕμ

Sequence icjp5p0a1lfpj

1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, 1, -1, 1, -1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, more...

integer, non-constant, non-monotonic, +-

a(n)=λ(ϕ(n))
ϕ(n)=Euler's totient function
λ(n)=Liouville's function
n≥1
3 operations
Prime
nϕλ
a(n)=λ(ϕ(n+abs(a(n-1))))
a(0)=1
ϕ(n)=Euler's totient function
λ(n)=Liouville's function
n≥0
6 operations
PrimeRecursive
nr|+ϕλ

Sequence vnkwwlsrv0tbf

1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 4, 2, 4, 2, 4, 4, 8, 2, 6, 4, 4, 4, 10, 4, 8, 4, 6, 4, 12, 4, 8, 8, 8, 8, 8, 4, 12, 6, 8, 8, 16, 4, 12, 8, 8, 10, 22, 8, 12, 8, more...

integer, non-constant, non-monotonic, +, A010554

a(n)=ϕ(ϕ(n))
ϕ(n)=Euler's totient function
n≥1
3 operations
Prime
nϕϕ

Sequence 5fvojtqjmm2dp

1, 1, 1, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 4, 1, 2, 1, 2, 2, 2, 1, 4, 2, 2, 2, 2, 1, 4, 1, 2, 2, 2, 2, 6, 1, 2, 2, 4, 1, 4, 1, 2, 2, 2, 1, 4, 2, 2, more...

integer, non-constant, non-monotonic, +, A163109

a(n)=ϕ(τ(n))
τ(n)=number of divisors of n
ϕ(n)=Euler's totient function
n≥1
3 operations
Prime
nτϕ

Sequence zvypkdkgsi1ep

1, 1, 1.4142135624, 1.4142135624, 2, 1.4142135624, 2.4494897428, 2, 2.4494897428, 2, 3.1622776602, 2, 3.4641016151, 2.4494897428, 2.8284271247, 2.8284271247, 4, 2.4494897428, 4.2426406871, 2.8284271247, 3.4641016151, 3.1622776602, 4.6904157598, 2.8284271247, 4.472135955, 3.4641016151, 4.2426406871, 3.4641016151, 5.2915026221, 2.8284271247, 5.4772255751, 4, 4.472135955, 4, 4.8989794856, 3.4641016151, 6, 4.2426406871, 4.8989794856, 4, 6.3245553203, 3.4641016151, 6.4807406984, 4.472135955, 4.8989794856, 4.6904157598, 6.7823299831, 4, 6.4807406984, 4.472135955, more...

decimal, non-constant, non-monotonic, +

a(n)=sqrt(ϕ(n))
ϕ(n)=Euler's totient function
n≥1
3 operations
Prime
nϕQ

Sequence gosfzvrwl0def

1, 1, 2, 2, 3, 2, 4, 3, 4, 3, 4, 3, 6, 4, 4, 4, 5, 4, 6, 4, 6, 4, 4, 4, 6, 6, 6, 6, 6, 4, 8, 5, 6, 5, 8, 6, 9, 6, 8, 5, 8, 6, 8, 6, 8, 4, 4, 5, 8, 6, more...

integer, non-constant, non-monotonic, +, A062821

a(n)=τ(ϕ(n))
ϕ(n)=Euler's totient function
τ(n)=number of divisors of n
n≥1
3 operations
Prime
nϕτ

Sequence 0jg0mjhedubal

1, 1, 2, 2, 24, 2, 720, 24, 720, 24, 3628800, 24, 479001600, 720, 40320, 40320, more...

integer, non-constant, non-monotonic, +

a(n)=ϕ(n)!
ϕ(n)=Euler's totient function
n≥1
3 operations
Prime
nϕ!

Sequence wtbrjntdusiqm

1.5574077247, 1.5574077247, -2.1850398633, -2.1850398633, 1.1578212823, -2.1850398633, -0.2910061914, 1.1578212823, -0.2910061914, 1.1578212823, 0.6483608275, 1.1578212823, -0.6358599287, -0.2910061914, -6.7997114552, -6.7997114552, 0.300632242, -0.2910061914, -1.1373137123, -6.7997114552, -0.6358599287, 0.6483608275, 0.008851656, -6.7997114552, 2.2371609442, -0.6358599287, -1.1373137123, -0.6358599287, -0.2814296046, -6.7997114552, -6.4053311966, 0.300632242, 2.2371609442, 0.300632242, -2.1348966977, -0.6358599287, 7.7504709057, -1.1373137123, -2.1348966977, 0.300632242, -1.1172149309, -0.6358599287, 2.2913879924, 2.2371609442, -2.1348966977, 0.008851656, -2.0866135311, 0.300632242, 2.2913879924, 2.2371609442, more...

decimal, non-constant, non-monotonic, +-

a(n)=tan(ϕ(n))
ϕ(n)=Euler's totient function
n≥1
3 operations
Prime
nϕW

Sequence rgi2swhi5uxv

2, 4, 6, 10, 12, 16, 18, 22, 28, 30, 36, 40, 42, 46, 52, 58, 60, 66, 70, 72, 78, 82, 88, 96, 100, 102, 106, 108, 112, 126, 130, 136, 138, 148, 150, 156, 162, 166, 172, 178, 180, 190, 192, 196, 198, 210, 222, 226, 228, 232, more...

integer, non-constant, strictly-monotonic, +

a(n)=ϕ(p(n))
p(n)=nth prime
ϕ(n)=Euler's totient function
n≥1
3 operations
Prime
npϕ

Sequence parunqhh2vuxb

2.7182818285, 2.7182818285, 7.3890560989, 7.3890560989, 54.5981500331, 7.3890560989, 403.4287934927, 54.5981500331, 403.4287934927, 54.5981500331, 22026.4657948067, 54.5981500331, 162754.7914190039, 403.4287934927, 2980.9579870417, 2980.9579870417, 8886110.520507872, 403.4287934927, 65659969.13733051, 2980.9579870417, 162754.7914190039, 22026.4657948067, 3584912846.131592, 2980.9579870417, 485165195.4097903, 162754.7914190039, 65659969.13733051, 162754.7914190039, more...

decimal, non-constant, non-monotonic, +

a(n)=exp(ϕ(n))
ϕ(n)=Euler's totient function
n≥1
3 operations
Prime
nϕe

Sequence t3dowyxopjzjc

3, 3, 5, 5, 11, 5, 17, 11, 17, 11, 31, 11, 41, 17, 23, 23, 59, 17, 67, 23, 41, 31, 83, 23, 73, 41, 67, 41, 109, 23, 127, 59, 73, 59, 97, 41, 157, 67, 97, 59, 179, 41, 191, 73, 97, 83, 211, 59, 191, 73, more...

integer, non-constant, non-monotonic, +

a(n)=p(ϕ(n))
ϕ(n)=Euler's totient function
p(n)=nth prime
n≥1
3 operations
Prime
nϕp

Sequence 1w3kesgurbqsm

-9, -9, -8, -8, -6, -8, -4, -6, -4, -6, 0, -6, 2, -4, -2, -2, 6, -4, 8, -2, 2, 0, 12, -2, 10, 2, 8, 2, 18, -2, 20, 6, 10, 6, 14, 2, 26, 8, 14, 6, 30, 2, 32, 10, 14, 12, 36, 6, 32, 10, more...

integer, non-constant, non-monotonic, +-0

a(n)=ϕ(n)-10
ϕ(n)=Euler's totient function
n≥1
4 operations
Prime
nϕ10-

Sequence wxih3dqngztol

-8, -8, -7, -7, -5, -7, -3, -5, -3, -5, 1, -5, 3, -3, -1, -1, 7, -3, 9, -1, 3, 1, 13, -1, 11, 3, 9, 3, 19, -1, 21, 7, 11, 7, 15, 3, 27, 9, 15, 7, 31, 3, 33, 11, 15, 13, 37, 7, 33, 11, more...

integer, non-constant, non-monotonic, +-

a(n)=ϕ(n)-9
ϕ(n)=Euler's totient function
n≥1
4 operations
Prime
nϕ9-

Sequence k4mkqcfexcomm

-7, -7, -6, -6, -4, -6, -2, -4, -2, -4, 2, -4, 4, -2, 0, 0, 8, -2, 10, 0, 4, 2, 14, 0, 12, 4, 10, 4, 20, 0, 22, 8, 12, 8, 16, 4, 28, 10, 16, 8, 32, 4, 34, 12, 16, 14, 38, 8, 34, 12, more...

integer, non-constant, non-monotonic, +-0

a(n)=ϕ(n)-8
ϕ(n)=Euler's totient function
n≥1
4 operations
Prime
nϕ8-

Sequence vk44aw2ahbnrg

-6, -6, -5, -5, -3, -5, -1, -3, -1, -3, 3, -3, 5, -1, 1, 1, 9, -1, 11, 1, 5, 3, 15, 1, 13, 5, 11, 5, 21, 1, 23, 9, 13, 9, 17, 5, 29, 11, 17, 9, 33, 5, 35, 13, 17, 15, 39, 9, 35, 13, more...

integer, non-constant, non-monotonic, +-

a(n)=ϕ(n)-7
ϕ(n)=Euler's totient function
n≥1
4 operations
Prime
nϕ7-

Sequence fu23tjaybn1dk

-5, -5, -4, -4, -2, -4, 0, -2, 0, -2, 4, -2, 6, 0, 2, 2, 10, 0, 12, 2, 6, 4, 16, 2, 14, 6, 12, 6, 22, 2, 24, 10, 14, 10, 18, 6, 30, 12, 18, 10, 34, 6, 36, 14, 18, 16, 40, 10, 36, 14, more...

integer, non-constant, non-monotonic, +-0

a(n)=ϕ(n)-6
ϕ(n)=Euler's totient function
n≥1
4 operations
Prime
nϕ6-

Sequence tgetzqa0otovh

-4, -4, -3, -3, -1, -3, 1, -1, 1, -1, 5, -1, 7, 1, 3, 3, 11, 1, 13, 3, 7, 5, 17, 3, 15, 7, 13, 7, 23, 3, 25, 11, 15, 11, 19, 7, 31, 13, 19, 11, 35, 7, 37, 15, 19, 17, 41, 11, 37, 15, more...

integer, non-constant, non-monotonic, +-

a(n)=ϕ(n)-5
ϕ(n)=Euler's totient function
n≥1
4 operations
Prime
nϕ5-

Sequence y14j0r2rllz1o

-3, -3, -5, -5, -11, -5, -17, -11, -17, -11, -31, -11, -41, -17, -23, -23, -59, -17, -67, -23, -41, -31, -83, -23, -73, -41, -67, -41, -109, -23, -127, -59, -73, -59, -97, -41, -157, -67, -97, -59, -179, -41, -191, -73, -97, -83, -211, -59, -191, -73, more...

integer, non-constant, non-monotonic, -

a(n)=-p(ϕ(n))
ϕ(n)=Euler's totient function
p(n)=nth prime
n≥1
4 operations
Prime
nϕp~

Sequence jbrqyfh0a23dh

-3, -3, -2, -2, 0, -2, 2, 0, 2, 0, 6, 0, 8, 2, 4, 4, 12, 2, 14, 4, 8, 6, 18, 4, 16, 8, 14, 8, 24, 4, 26, 12, 16, 12, 20, 8, 32, 14, 20, 12, 36, 8, 38, 16, 20, 18, 42, 12, 38, 16, more...

integer, non-constant, non-monotonic, +-0

a(n)=ϕ(n)-4
ϕ(n)=Euler's totient function
n≥1
4 operations
Prime
nϕ4-

Sequence yk10uj5rmiei

-2.7182818285, -2.7182818285, -7.3890560989, -7.3890560989, -54.5981500331, -7.3890560989, -403.4287934927, -54.5981500331, -403.4287934927, -54.5981500331, -22026.4657948067, -54.5981500331, -162754.7914190039, -403.4287934927, -2980.9579870417, -2980.9579870417, -8886110.520507872, -403.4287934927, -65659969.13733051, -2980.9579870417, -162754.7914190039, -22026.4657948067, -3584912846.131592, -2980.9579870417, -485165195.4097903, -162754.7914190039, -65659969.13733051, -162754.7914190039, more...

decimal, non-constant, non-monotonic, -

a(n)=-exp(ϕ(n))
ϕ(n)=Euler's totient function
n≥1
4 operations
Prime
nϕe~

Sequence tefgnawkguohj

-2.1850398633, 1.1578212823, -0.2910061914, 0.6483608275, -0.6358599287, 0.300632242, -1.1373137123, 0.008851656, -0.2814296046, -6.4053311966, 7.7504709057, -1.1172149309, 2.2913879924, -2.0866135311, -6.0532723828, 8.3308568525, 0.3200403894, 0.0265605178, 1.2219599181, -0.2624173775, -0.5991799983, 0.3298264065, 0.0354205013, -5.4513401108, -0.5872139152, 9.7929802635, -1.0592232275, 2.4681619616, -1.9518769927, 0.349572426, 2.5323384275, 1.2904015647, -0.2342243299, 0.3595365943, -1.0223462354, -1.869564997, -4.7386661503, -0.5520433399, -1.004405257, -1.8304221492, 1.3386902104, 15.0482062261, 0.3796580018, 2.7434221201, 0.0798317705, -0.5291666917, -1.7558165729, -0.1971680547, -4.1853335779, -0.5178892416, more...

decimal, non-constant, non-monotonic, +-

a(n)=tan(ϕ(p(n)))
p(n)=nth prime
ϕ(n)=Euler's totient function
n≥1
4 operations
Prime
npϕW

Sequence udao1wsboetg

-2.1415926536, -2.1415926536, -1.1415926536, -1.1415926536, 0.8584073464, -1.1415926536, 2.8584073464, 0.8584073464, 2.8584073464, 0.8584073464, 6.8584073464, 0.8584073464, 8.8584073464, 2.8584073464, 4.8584073464, 4.8584073464, 12.8584073464, 2.8584073464, 14.8584073464, 4.8584073464, 8.8584073464, 6.8584073464, 18.8584073464, 4.8584073464, 16.8584073464, 8.8584073464, 14.8584073464, 8.8584073464, 24.8584073464, 4.8584073464, 26.8584073464, 12.8584073464, 16.8584073464, 12.8584073464, 20.8584073464, 8.8584073464, 32.8584073464, 14.8584073464, 20.8584073464, 12.8584073464, 36.8584073464, 8.8584073464, 38.8584073464, 16.8584073464, 20.8584073464, 18.8584073464, 42.8584073464, 12.8584073464, 38.8584073464, 16.8584073464, more...

decimal, non-constant, non-monotonic, +-

a(n)=ϕ(n)-π
ϕ(n)=Euler's totient function
Pi (3.141...)
n≥1
4 operations
Prime
nϕπ-

Sequence rltaur2du2wij

-2, -4, -6, -10, -12, -16, -18, -22, -28, -30, -36, -40, -42, -46, -52, -58, -60, -66, -70, -72, -78, -82, -88, -96, -100, -102, -106, -108, -112, -126, -130, -136, -138, -148, -150, -156, -162, -166, -172, -178, -180, -190, -192, -196, -198, -210, -222, -226, -228, -232, more...

integer, non-constant, strictly-monotonic, -

a(n)=-ϕ(p(n))
p(n)=nth prime
ϕ(n)=Euler's totient function
n≥1
4 operations
Prime
npϕ~

Sequence vtupyfruyzyhd

-2, -2, -1, -1, 1, -1, 3, 1, 3, 1, 7, 1, 9, 3, 5, 5, 13, 3, 15, 5, 9, 7, 19, 5, 17, 9, 15, 9, 25, 5, 27, 13, 17, 13, 21, 9, 33, 15, 21, 13, 37, 9, 39, 17, 21, 19, 43, 13, 39, 17, more...

integer, non-constant, non-monotonic, +-

a(n)=ϕ(n)-3
ϕ(n)=Euler's totient function
n≥1
4 operations
Prime
nϕ3-

Sequence aox22zq2iw05d

-1.5574077247, -1.5574077247, 2.1850398633, 2.1850398633, -1.1578212823, 2.1850398633, 0.2910061914, -1.1578212823, 0.2910061914, -1.1578212823, -0.6483608275, -1.1578212823, 0.6358599287, 0.2910061914, 6.7997114552, 6.7997114552, -0.300632242, 0.2910061914, 1.1373137123, 6.7997114552, 0.6358599287, -0.6483608275, -0.008851656, 6.7997114552, -2.2371609442, 0.6358599287, 1.1373137123, 0.6358599287, 0.2814296046, 6.7997114552, 6.4053311966, -0.300632242, -2.2371609442, -0.300632242, 2.1348966977, 0.6358599287, -7.7504709057, 1.1373137123, 2.1348966977, -0.300632242, 1.1172149309, 0.6358599287, -2.2913879924, -2.2371609442, 2.1348966977, -0.008851656, 2.0866135311, -0.300632242, -2.2913879924, -2.2371609442, more...

decimal, non-constant, non-monotonic, +-

a(n)=tan(-ϕ(n))
ϕ(n)=Euler's totient function
n≥1
4 operations
Prime
nϕ~W

Sequence c3bn3ly4vya4l

-1, -1, -2, -2, -24, -2, -720, -24, -720, -24, -3628800, -24, -479001600, -720, -40320, -40320, more...

integer, non-constant, non-monotonic, -

a(n)=-ϕ(n)!
ϕ(n)=Euler's totient function
n≥1
4 operations
Prime
nϕ!~

Sequence vivrpjhqvsiwd

-1, -1, -2, -2, -3, -2, -4, -3, -4, -3, -4, -3, -6, -4, -4, -4, -5, -4, -6, -4, -6, -4, -4, -4, -6, -6, -6, -6, -6, -4, -8, -5, -6, -5, -8, -6, -9, -6, -8, -5, -8, -6, -8, -6, -8, -4, -4, -5, -8, -6, more...

integer, non-constant, non-monotonic, -

a(n)=-τ(ϕ(n))
ϕ(n)=Euler's totient function
τ(n)=number of divisors of n
n≥1
4 operations
Prime
nϕτ~

Sequence o023cndecoloc

-1, -1, -1.4142135624, -1.4142135624, -2, -1.4142135624, -2.4494897428, -2, -2.4494897428, -2, -3.1622776602, -2, -3.4641016151, -2.4494897428, -2.8284271247, -2.8284271247, -4, -2.4494897428, -4.2426406871, -2.8284271247, -3.4641016151, -3.1622776602, -4.6904157598, -2.8284271247, -4.472135955, -3.4641016151, -4.2426406871, -3.4641016151, -5.2915026221, -2.8284271247, -5.4772255751, -4, -4.472135955, -4, -4.8989794856, -3.4641016151, -6, -4.2426406871, -4.8989794856, -4, -6.3245553203, -3.4641016151, -6.4807406984, -4.472135955, -4.8989794856, -4.6904157598, -6.7823299831, -4, -6.4807406984, -4.472135955, more...

decimal, non-constant, non-monotonic, -

a(n)=-sqrt(ϕ(n))
ϕ(n)=Euler's totient function
n≥1
4 operations
Prime
nϕQ~

Sequence y2npetz5reokp

-1, -1, -1, -2, -1, -2, -1, -2, -2, -2, -1, -2, -1, -2, -2, -4, -1, -2, -1, -2, -2, -2, -1, -4, -2, -2, -2, -2, -1, -4, -1, -2, -2, -2, -2, -6, -1, -2, -2, -4, -1, -4, -1, -2, -2, -2, -1, -4, -2, -2, more...

integer, non-constant, non-monotonic, -

a(n)=-ϕ(τ(n))
τ(n)=number of divisors of n
ϕ(n)=Euler's totient function
n≥1
4 operations
Prime
nτϕ~

Sequence ongm0zjzeqhm

-1, -1, -1, -1, -2, -1, -2, -2, -2, -2, -4, -2, -4, -2, -4, -4, -8, -2, -6, -4, -4, -4, -10, -4, -8, -4, -6, -4, -12, -4, -8, -8, -8, -8, -8, -4, -12, -6, -8, -8, -16, -4, -12, -8, -8, -10, -22, -8, -12, -8, more...

integer, non-constant, non-monotonic, -

a(n)=-ϕ(ϕ(n))
ϕ(n)=Euler's totient function
n≥1
4 operations
Prime
nϕϕ~

Sequence xum1nydpgqwcm

-1, -1, 0, 0, 2, 0, 4, 2, 4, 2, 8, 2, 10, 4, 6, 6, 14, 4, 16, 6, 10, 8, 20, 6, 18, 10, 16, 10, 26, 6, 28, 14, 18, 14, 22, 10, 34, 16, 22, 14, 38, 10, 40, 18, 22, 20, 44, 14, 40, 18, more...

integer, non-constant, non-monotonic, +-0

a(n)=ϕ(n)-2
ϕ(n)=Euler's totient function
n≥1
4 operations
Prime
nϕ2-

Sequence kz5alianxhcbf

-1, -1, 1, 1, -1, 1, -1, -1, -1, -1, -1, -1, 1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, 1, -1, 1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, 1, 1, more...

integer, non-constant, non-monotonic, +-

a(n)=-λ(ϕ(n))
ϕ(n)=Euler's totient function
λ(n)=Liouville's function
n≥1
4 operations
Prime
nϕλ~

Sequence fvejnqoyiek1h

-1, -1, 1, 1, 0, 1, -1, 0, -1, 0, -1, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, -1, 0, 1, 0, more...

integer, non-constant, non-monotonic, +-0

a(n)=-μ(ϕ(n))
ϕ(n)=Euler's totient function
μ(n)=Möbius function
n≥1
4 operations
Prime
nϕμ~

Sequence iceidapelmvdm

-0.9899924966, -0.9899924966, 0.2836621855, 0.2836621855, 0.004425698, 0.2836621855, -0.2751633381, 0.004425698, -0.2751633381, 0.004425698, 0.9147423578, 0.004425698, -0.9873392775, -0.2751633381, -0.5328330203, -0.5328330203, -0.771080223, -0.2751633381, -0.5177697998, -0.5328330203, -0.9873392775, 0.9147423578, 0.249540118, -0.5328330203, -0.7361927182, -0.9873392775, -0.5177697998, -0.9873392775, -0.5770021789, -0.5328330203, 0.232359102, -0.771080223, -0.7361927182, -0.771080223, -0.9251475366, -0.9873392775, 0.9968309934, -0.5177697998, -0.9251475366, -0.771080223, -0.9974960527, -0.9873392775, -0.8037933932, -0.7361927182, -0.9251475366, 0.249540118, -0.8711325991, -0.771080223, -0.8037933932, -0.7361927182, more...

decimal, non-constant, non-monotonic, +-

a(n)=cos(p(ϕ(n)))
ϕ(n)=Euler's totient function
p(n)=nth prime
n≥1
4 operations
Prime
nϕpO

Sequence wnowc2dssdvzj

-0.9117339148, -0.9117339148, 0.4483562418, 0.4483562418, -0.3706617334, 0.4483562418, 0.2627415567, -0.3706617334, 0.2627415567, -0.3706617334, -0.725042318, -0.3706617334, 0.128036763, 0.2627415567, -0.9157436949, -0.9157436949, -0.8581715487, 0.2627415567, -0.5803010704, -0.9157436949, 0.128036763, -0.725042318, 0.9952748137, -0.9157436949, 0.9162170329, 0.128036763, -0.5803010704, 0.128036763, more...

decimal, non-constant, non-monotonic, +-

a(n)=cos(exp(ϕ(n)))
ϕ(n)=Euler's totient function
n≥1
4 operations
Prime
nϕeO

Sequence yni5ns5croxal

-0.8414709848, -0.8414709848, -0.9092974268, -0.9092974268, 0.7568024953, -0.9092974268, 0.2794154982, 0.7568024953, 0.2794154982, 0.7568024953, 0.5440211109, 0.7568024953, 0.536572918, 0.2794154982, -0.9893582466, -0.9893582466, 0.2879033167, 0.2794154982, 0.7509872468, -0.9893582466, 0.536572918, 0.5440211109, 0.0088513093, -0.9893582466, -0.9129452507, 0.536572918, 0.7509872468, 0.536572918, -0.2709057883, -0.9893582466, 0.9880316241, 0.2879033167, -0.9129452507, 0.2879033167, 0.905578362, 0.536572918, 0.9917788534, 0.7509872468, 0.905578362, 0.2879033167, -0.7451131605, 0.536572918, 0.9165215479, -0.9129452507, 0.905578362, 0.0088513093, -0.9017883476, 0.2879033167, 0.9165215479, -0.9129452507, more...

decimal, non-constant, non-monotonic, +-

a(n)=sin(-ϕ(n))
ϕ(n)=Euler's totient function
n≥1
4 operations
Prime
nϕ~S

Sequence v44gbnyigtnuk

-0.5403023059, -0.5403023059, 0.4161468365, 0.4161468365, 0.6536436209, 0.4161468365, -0.9601702867, 0.6536436209, -0.9601702867, 0.6536436209, 0.8390715291, 0.6536436209, -0.8438539587, -0.9601702867, 0.1455000338, 0.1455000338, 0.9576594803, -0.9601702867, -0.6603167082, 0.1455000338, -0.8438539587, 0.8390715291, 0.9999608264, 0.1455000338, -0.4080820618, -0.8438539587, -0.6603167082, -0.8438539587, 0.9626058663, 0.1455000338, -0.1542514499, 0.9576594803, -0.4080820618, 0.9576594803, -0.4241790073, -0.8438539587, 0.1279636896, -0.6603167082, -0.4241790073, 0.9576594803, 0.6669380617, -0.8438539587, 0.399985315, -0.4080820618, -0.4241790073, 0.9999608264, 0.4321779449, 0.9576594803, 0.399985315, -0.4080820618, more...

decimal, non-constant, non-monotonic, +-

a(n)=-cos(ϕ(n))
ϕ(n)=Euler's totient function
n≥1
4 operations
Prime
nϕO~

Sequence v1vegdrzneyle

-0.4505495341, -0.4505495341, 1.9936266556, 1.9936266556, 2.5057022416, 1.9936266556, 3.67230163, 2.5057022416, 3.67230163, 2.5057022416, 0.9498815456, 2.5057022416, 7.745973886, 3.67230163, -0.4387286244, -0.4387286244, -0.5982055959, 3.67230163, 1.4034129392, -0.4387286244, 7.745973886, 0.9498815456, 0.0975591069, -0.4387286244, 0.4373225333, 7.745973886, 1.4034129392, 7.745973886, more...

decimal, non-constant, non-monotonic, +-

a(n)=tan(exp(ϕ(n)))
ϕ(n)=Euler's totient function
n≥1
4 operations
Prime
nϕeW

Sequence m2ptwa5j5e4pb

-0.4161468365, -0.6536436209, 0.9601702867, -0.8390715291, 0.8438539587, -0.9576594803, 0.6603167082, -0.9999608264, -0.9626058663, 0.1542514499, -0.1279636896, -0.6669380617, -0.399985315, -0.4321779449, -0.1629907808, 0.1191801354, -0.9524129804, -0.999647456, 0.6333192031, -0.9672505883, -0.8578030932, 0.9496776979, 0.9993732837, -0.1804304493, 0.8623188723, 0.1015857037, 0.6864865509, 0.3755095978, 0.4559691044, 0.9439841392, -0.3672913305, -0.6125482395, 0.973648893, -0.941026309, 0.6992508065, 0.4716522936, 0.2064822293, -0.875459459, -0.7055510067, -0.4794387656, -0.5984600691, 0.0663068584, -0.9348897059, 0.3424664577, -0.996828595, -0.8838774732, -0.4948984146, 0.9811113543, -0.2323884212, 0.8879827698, more...

decimal, non-constant, non-monotonic, +-

a(n)=cos(ϕ(p(n)))
p(n)=nth prime
ϕ(n)=Euler's totient function
n≥1
4 operations
Prime
npϕO

Sequence 0wrfy32p2vrim

-0.1425465431, -0.1425465431, -3.3805150062, -3.3805150062, -225.9508464542, -3.3805150062, 3.4939156455, -225.9508464542, 3.4939156455, -225.9508464542, -0.441695568, -225.9508464542, 0.1606566987, 3.4939156455, 1.5881530834, 1.5881530834, -0.8257740092, 3.4939156455, 1.652317264, 1.5881530834, 0.1606566987, -0.441695568, 3.8805963104, 1.5881530834, 0.9192864044, 0.1606566987, 1.652317264, 0.1606566987, -1.4154931063, 1.5881530834, 4.1858918319, -0.8257740092, 0.9192864044, -0.8257740092, -0.410321299, 0.1606566987, -0.0798014341, 1.652317264, -0.410321299, -0.8257740092, -0.0708996963, 0.1606566987, -0.7401261985, 0.9192864044, -0.410321299, 3.8805963104, 0.5636889887, -0.8257740092, -0.7401261985, 0.9192864044, more...

decimal, non-constant, non-monotonic, +-

a(n)=tan(p(ϕ(n)))
ϕ(n)=Euler's totient function
p(n)=nth prime
n≥1
4 operations
Prime
nϕpW

Sequence ujniiarjil3pg

0, -1, -2, -4, -6, -10, -12, -18, -22, -28, -32, -42, -46, -58, -64, -72, -80, -96, -102, -120, -128, -140, -150, -172, -180, -200, -212, -230, -242, -270, -278, -308, -324, -344, -360, -384, -396, -432, -450, -474, -490, -530, -542, -584, -604, -628, -650, -696, -712, -754, more...

integer, non-constant, strictly-monotonic, -0

a(n)=a(n-1)-ϕ(n)
a(0)=0
ϕ(n)=Euler's totient function
n≥0
4 operations
PrimeRecursive
rnϕ-

Sequence ybxldy14izrhj

0, -1, -1, -2, -1, -4, -1, -4, -3, -6, -1, -8, -1, -8, -7, -8, -1, -12, -1, -12, -9, -12, -1, -16, -5, -14, -9, -16, -1, -22, -1, -16, -13, -18, -11, -24, -1, -20, -15, -24, -1, -30, -1, -24, -21, -24, -1, -32, -7, -30, more...

integer, non-constant, non-monotonic, -0

a(n)=ϕ(n)-n
ϕ(n)=Euler's totient function
n≥1
4 operations
Prime
nϕn-

Sequence haxmjfjemljqi

0, -1, -1, -1, -1, -1, -1, -2, -1, -1, -1, -2, -1, -1, -1, -2, -1, -2, -1, -2, -1, -1, -1, -2, -1, -1, -2, -2, -1, -2, -1, -4, -1, -1, -1, -2, -1, -1, -1, -2, -1, -2, -1, -2, -2, -1, -1, -4, -1, -2, more...

integer, non-constant, non-monotonic, -0

a(n)=-ϕ(Ω(n))
Ω(n)=max factorization terms
ϕ(n)=Euler's totient function
n≥1
4 operations
Prime
nΩϕ~

Sequence trmlrn5ecnoyk

0, 0, -1, -1, -3, -1, -5, -3, -5, -3, -9, -3, -11, -5, -7, -7, -15, -5, -17, -7, -11, -9, -21, -7, -19, -11, -17, -11, -27, -7, -29, -15, -19, -15, -23, -11, -35, -17, -23, -15, -39, -11, -41, -19, -23, -21, -45, -15, -41, -19, more...

integer, non-constant, non-monotonic, -0

a(n)=1-ϕ(n)
ϕ(n)=Euler's totient function
n≥1
4 operations
Prime
1nϕ-

Sequence qckxsgjjsseio

0, 0, -1, -1, -2, -1, -2, -2, -2, -2, -2, -2, -3, -2, -3, -3, -4, -2, -3, -3, -3, -2, -2, -3, -3, -3, -3, -3, -3, -3, -3, -4, -3, -4, -4, -3, -4, -3, -4, -4, -4, -3, -3, -3, -4, -2, -2, -4, -3, -3, more...

integer, non-constant, non-monotonic, -0

a(n)=-Ω(ϕ(n))
ϕ(n)=Euler's totient function
Ω(n)=max factorization terms
n≥1
4 operations
Prime
nϕΩ~

Sequence co44hcqtza3vl

0, 0, -1, -1, -1, -1, 0, -1, 0, -1, -1, -1, 0, 0, -1, -1, -1, 0, 0, -1, 0, -1, -1, -1, 0, 0, 0, 0, -1, -1, 0, -1, 0, -1, 0, 0, -1, 0, 0, -1, -1, 0, -1, 0, 0, -1, -1, -1, -1, 0, more...

integer, non-constant, non-monotonic, -0

a(n)=floor(cos(ϕ(n)))
ϕ(n)=Euler's totient function
n≥1
4 operations
Prime
nϕOf

Sequence tmcgussbypodl

0, 0, -0.6931471806, -0.6931471806, -1.3862943611, -0.6931471806, -1.7917594692, -1.3862943611, -1.7917594692, -1.3862943611, -2.302585093, -1.3862943611, -2.4849066498, -1.7917594692, -2.0794415417, -2.0794415417, -2.7725887222, -1.7917594692, -2.8903717579, -2.0794415417, -2.4849066498, -2.302585093, -3.0910424534, -2.0794415417, -2.9957322736, -2.4849066498, -2.8903717579, -2.4849066498, -3.3322045102, -2.0794415417, -3.4011973817, -2.7725887222, -2.9957322736, -2.7725887222, -3.1780538303, -2.4849066498, -3.5835189385, -2.8903717579, -3.1780538303, -2.7725887222, -3.6888794541, -2.4849066498, -3.7376696183, -2.9957322736, -3.1780538303, -3.0910424534, -3.8286413965, -2.7725887222, -3.7376696183, -2.9957322736, more...

decimal, non-constant, non-monotonic, -0

a(n)=-ln(ϕ(n))
ϕ(n)=Euler's totient function
n≥1
4 operations
Prime
nϕl~

Sequence d2542j0fymq5n

0, 0, -0.6931471806, -0.6931471806, -0.6931471806, -0.6931471806, 0, -0.6931471806, 0, -0.6931471806, 0, -0.6931471806, 0, 0, -0.6931471806, -0.6931471806, -0.6931471806, 0, 0, -0.6931471806, 0, 0, 0, -0.6931471806, 0, 0, 0, 0, 0, -0.6931471806, 0, -0.6931471806, 0, -0.6931471806, 0, 0, 0, 0, 0, -0.6931471806, 0, 0, 0, 0, 0, 0, 0, -0.6931471806, 0, 0, more...

decimal, non-constant, non-monotonic, -0

a(n)=-Λ(ϕ(n))
ϕ(n)=Euler's totient function
Λ(n)=Von Mangoldt's function
n≥1
4 operations
Prime
nϕΛ~

Sequence 20yqzfhximqlb

0, 0, 0, 0, -1, 0, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, -1, -1, -1, 0, -1, -1, -1, 0, 0, -1, -1, -1, 0, 0, -1, -1, 0, -1, -1, -1, -1, -1, -1, -1, 0, -1, -1, 0, -1, -1, 0, -1, -1, 0, more...

integer, non-constant, non-monotonic, -0

a(n)=floor(sin(ϕ(n)))
ϕ(n)=Euler's totient function
n≥1
4 operations
Prime
nϕSf

Sequence stx3x3t4vuuzn

0, 0, 0, 0, 0, 0, 0.6931471806, 0, 0, 0, 0.6931471806, 0, 0, 0, 0.6931471806, 0, 0.6931471806, 0, 0.6931471806, 0, 0, 0, 0.6931471806, 0, 0, 0.6931471806, 0.6931471806, 0, 0.6931471806, 0, 1.3862943611, 0, 0, 0, 0.6931471806, 0, 0, 0, 0.6931471806, 0, 0.6931471806, 0, 0.6931471806, 0.6931471806, 0, 0, 1.3862943611, 0, 0.6931471806, 0, more...

decimal, non-constant, non-monotonic, +0

a(n)=ln(ϕ(Ω(n)))
Ω(n)=max factorization terms
ϕ(n)=Euler's totient function
n≥2
4 operations
Prime
nΩϕl

Sequence mtri3xpf4tski

0, 0, 0, 0, 0.6931471806, 0, 0.6931471806, 0.6931471806, 0.6931471806, 0.6931471806, 0.6931471806, 0.6931471806, 0.6931471806, 0.6931471806, 0.6931471806, 0.6931471806, 0.6931471806, 0.6931471806, 0, 0.6931471806, 0.6931471806, 0.6931471806, 0, 0.6931471806, 0.6931471806, 0.6931471806, 0, 0.6931471806, 0, 0.6931471806, 0.6931471806, 0.6931471806, 0.6931471806, 0.6931471806, 0.6931471806, 0.6931471806, 0, 0, 0.6931471806, 0.6931471806, 0.6931471806, 0.6931471806, 0, 0.6931471806, 0.6931471806, 0, 0, 0.6931471806, 0, 0.6931471806, more...

decimal, non-constant, non-monotonic, +0

a(n)=Λ(ϕ(ϕ(n)))
ϕ(n)=Euler's totient function
Λ(n)=Von Mangoldt's function
n≥1
4 operations
Prime
nϕϕΛ

Sequence 1ezgv2c4g551f

0, 0, 0, 0, 0.6931471806, 0, 0.6931471806, 0.6931471806, 0.6931471806, 0.6931471806, 0.6931471806, 0.6931471806, 1.0986122887, 0.6931471806, 1.0986122887, 1.0986122887, 0.6931471806, 0.6931471806, 1.0986122887, 1.0986122887, 1.0986122887, 0.6931471806, 0.6931471806, 1.0986122887, 1.0986122887, 1.0986122887, 1.0986122887, 1.0986122887, 1.0986122887, 1.0986122887, 1.0986122887, 0.6931471806, 1.0986122887, 0.6931471806, 0.6931471806, 1.0986122887, 0.6931471806, 1.0986122887, 0.6931471806, 0.6931471806, 0.6931471806, 1.0986122887, 1.0986122887, 1.0986122887, 0.6931471806, 0.6931471806, 0.6931471806, 0.6931471806, 1.0986122887, 1.0986122887, more...

decimal, non-constant, non-monotonic, +0

a(n)=Λ(Ω(ϕ(n)))
ϕ(n)=Euler's totient function
Ω(n)=max factorization terms
Λ(n)=Von Mangoldt's function
n≥1
4 operations
Prime
nϕΩΛ

Sequence lc4tfmt3u5j1p

0, 0, 0, 0, 0.6931471806, 0, 0.6931471806, 0.6931471806, 0.6931471806, 0.6931471806, 1.3862943611, 0.6931471806, 1.3862943611, 0.6931471806, 1.3862943611, 1.3862943611, 2.0794415417, 0.6931471806, 1.7917594692, 1.3862943611, 1.3862943611, 1.3862943611, 2.302585093, 1.3862943611, 2.0794415417, 1.3862943611, 1.7917594692, 1.3862943611, 2.4849066498, 1.3862943611, 2.0794415417, 2.0794415417, 2.0794415417, 2.0794415417, 2.0794415417, 1.3862943611, 2.4849066498, 1.7917594692, 2.0794415417, 2.0794415417, 2.7725887222, 1.3862943611, 2.4849066498, 2.0794415417, 2.0794415417, 2.302585093, 3.0910424534, 2.0794415417, 2.4849066498, 2.0794415417, more...

decimal, non-constant, non-monotonic, +0

a(n)=ln(ϕ(ϕ(n)))
ϕ(n)=Euler's totient function
n≥1
4 operations
Prime
nϕϕl

Sequence x20lwqkdwazpl

0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, more...

integer, non-constant, non-monotonic, +0

a(n)=Ω(Ω(ϕ(n)))
ϕ(n)=Euler's totient function
Ω(n)=max factorization terms
n≥1
4 operations
Prime
nϕΩΩ

Sequence neye513wgk1og

0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 2, 1, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 3, 2, 3, 2, 2, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 3, 3, 2, 3, 2, more...

integer, non-constant, non-monotonic, +0

a(n)=floor(ln(ϕ(n)))
ϕ(n)=Euler's totient function
n≥1
4 operations
Prime
nϕlf

Sequence xrdkxuiogghcl

0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 2, 1, 2, 1, 2, 2, 3, 1, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 3, 2, 3, 3, 3, 3, 3, 2, 3, 2, 3, 3, 4, 2, 3, 3, 3, 2, 2, 3, 3, 3, more...

integer, non-constant, non-monotonic, +0

a(n)=Ω(ϕ(ϕ(n)))
ϕ(n)=Euler's totient function
Ω(n)=max factorization terms
n≥1
4 operations
Prime
nϕϕΩ

Sequence prhaibd5kipil

0, 0, 0, 0.6931471806, 0, 0.6931471806, 0, 0.6931471806, 0.6931471806, 0.6931471806, 0, 0.6931471806, 0, 0.6931471806, 0.6931471806, 0.6931471806, 0, 0.6931471806, 0, 0.6931471806, 0.6931471806, 0.6931471806, 0, 0.6931471806, 0.6931471806, 0.6931471806, 0.6931471806, 0.6931471806, 0, 0.6931471806, 0, 0.6931471806, 0.6931471806, 0.6931471806, 0.6931471806, 0, 0, 0.6931471806, 0.6931471806, 0.6931471806, 0, 0.6931471806, 0, 0.6931471806, 0.6931471806, 0.6931471806, 0, 0.6931471806, 0.6931471806, 0.6931471806, more...

decimal, non-constant, non-monotonic, +0

a(n)=Λ(ϕ(τ(n)))
τ(n)=number of divisors of n
ϕ(n)=Euler's totient function
Λ(n)=Von Mangoldt's function
n≥1
4 operations
Prime
nτϕΛ

Sequence fjzgs0c42stte

0, 0, 0, 0.6931471806, 0, 0.6931471806, 0, 0.6931471806, 0.6931471806, 0.6931471806, 0, 0.6931471806, 0, 0.6931471806, 0.6931471806, 1.3862943611, 0, 0.6931471806, 0, 0.6931471806, 0.6931471806, 0.6931471806, 0, 1.3862943611, 0.6931471806, 0.6931471806, 0.6931471806, 0.6931471806, 0, 1.3862943611, 0, 0.6931471806, 0.6931471806, 0.6931471806, 0.6931471806, 1.7917594692, 0, 0.6931471806, 0.6931471806, 1.3862943611, 0, 1.3862943611, 0, 0.6931471806, 0.6931471806, 0.6931471806, 0, 1.3862943611, 0.6931471806, 0.6931471806, more...

decimal, non-constant, non-monotonic, +0

a(n)=ln(ϕ(τ(n)))
τ(n)=number of divisors of n
ϕ(n)=Euler's totient function
n≥1
4 operations
Prime
nτϕl

Sequence ohz4b3omzj2vh

0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 2, 0, 1, 0, 1, 1, 1, 0, 2, 1, 1, 1, 1, 0, 2, 0, 1, 1, 1, 1, 2, 0, 1, 1, 2, 0, 2, 0, 1, 1, 1, 0, 2, 1, 1, more...

integer, non-constant, non-monotonic, +0

a(n)=Ω(ϕ(τ(n)))
τ(n)=number of divisors of n
ϕ(n)=Euler's totient function
Ω(n)=max factorization terms
n≥1
4 operations
Prime
nτϕΩ

Sequence fw1crqnz0ugyh

0, 0, 0.3465735903, 0.3465735903, 0.6931471806, 0.3465735903, 0.8958797346, 0.6931471806, 0.8958797346, 0.6931471806, 1.1512925465, 0.6931471806, 1.2424533249, 0.8958797346, 1.0397207708, 1.0397207708, 1.3862943611, 0.8958797346, 1.4451858789, 1.0397207708, 1.2424533249, 1.1512925465, 1.5455212267, 1.0397207708, 1.4978661368, 1.2424533249, 1.4451858789, 1.2424533249, 1.6661022551, 1.0397207708, 1.7005986908, 1.3862943611, 1.4978661368, 1.3862943611, 1.5890269152, 1.2424533249, 1.7917594692, 1.4451858789, 1.5890269152, 1.3862943611, 1.8444397271, 1.2424533249, 1.8688348091, 1.4978661368, 1.5890269152, 1.5455212267, 1.9143206982, 1.3862943611, 1.8688348091, 1.4978661368, more...

decimal, non-constant, non-monotonic, +0

a(n)=ln(sqrt(ϕ(n)))
ϕ(n)=Euler's totient function
n≥1
4 operations
Prime
nϕQl

Sequence sjdby0lz00v0m

0, 0, 0.6389612763, 0.6389612763, 0.6389612763, 0.6389612763, 0, 0.6389612763, 0, 0.6389612763, 0, 0.6389612763, 0, 0, 0.6389612763, 0.6389612763, 0.6389612763, 0, 0, 0.6389612763, 0, 0, 0, 0.6389612763, 0, 0, 0, 0, 0, 0.6389612763, 0, 0.6389612763, 0, 0.6389612763, 0, 0, 0, 0, 0, 0.6389612763, 0, 0, 0, 0, 0, 0, 0, 0.6389612763, 0, 0, more...

decimal, non-constant, non-monotonic, +0

a(n)=sin(Λ(ϕ(n)))
ϕ(n)=Euler's totient function
Λ(n)=Von Mangoldt's function
n≥1
4 operations
Prime
nϕΛS

Sequence ouk3jjed2jnme

0, 0, 0.6389612763, 0.6389612763, 0.9830277404, 0.6389612763, 0.9756868105, 0.9830277404, 0.9756868105, 0.9830277404, 0.743980337, 0.9830277404, 0.6104954587, 0.9756868105, 0.8734050818, 0.8734050818, 0.3606865907, 0.9756868105, 0.2485867156, 0.8734050818, 0.6104954587, 0.743980337, 0.0505286743, 0.8734050818, 0.1453437273, 0.6104954587, 0.2485867156, 0.6104954587, -0.1894597053, 0.8734050818, -0.256698545, 0.3606865907, 0.1453437273, 0.3606865907, -0.0364530986, 0.6104954587, -0.4276814832, 0.2485867156, -0.0364530986, 0.3606865907, -0.5203722388, 0.6104954587, -0.561400316, 0.1453437273, -0.0364530986, 0.0505286743, -0.6342582682, 0.3606865907, -0.561400316, 0.1453437273, more...

decimal, non-constant, non-monotonic, +-0

a(n)=sin(ln(ϕ(n)))
ϕ(n)=Euler's totient function
n≥1
4 operations
Prime
nϕlS

Sequence kdgo5st3fjgvl

0, 0, 0.6931471806, 0.6931471806, 1.0986122887, 0.6931471806, 0.6931471806, 1.0986122887, 0.6931471806, 1.0986122887, 0.6931471806, 1.0986122887, 0, 0.6931471806, 0.6931471806, 0.6931471806, 1.6094379124, 0.6931471806, 0, 0.6931471806, 0, 0.6931471806, 0.6931471806, 0.6931471806, 0, 0, 0, 0, 0, 0.6931471806, 0.6931471806, 1.6094379124, 0, 1.6094379124, 0.6931471806, 0, 1.0986122887, 0, 0.6931471806, 1.6094379124, 0.6931471806, 0, 0.6931471806, 0, 0.6931471806, 0.6931471806, 0.6931471806, 1.6094379124, 0.6931471806, 0, more...

decimal, non-constant, non-monotonic, +0

a(n)=Λ(τ(ϕ(n)))
ϕ(n)=Euler's totient function
τ(n)=number of divisors of n
Λ(n)=Von Mangoldt's function
n≥1
4 operations
Prime
nϕτΛ

Sequence sa4ebqyhc5nbd

0, 0, 0.6931471806, 0.6931471806, 1.0986122887, 0.6931471806, 1.3862943611, 1.0986122887, 1.3862943611, 1.0986122887, 1.3862943611, 1.0986122887, 1.7917594692, 1.3862943611, 1.3862943611, 1.3862943611, 1.6094379124, 1.3862943611, 1.7917594692, 1.3862943611, 1.7917594692, 1.3862943611, 1.3862943611, 1.3862943611, 1.7917594692, 1.7917594692, 1.7917594692, 1.7917594692, 1.7917594692, 1.3862943611, 2.0794415417, 1.6094379124, 1.7917594692, 1.6094379124, 2.0794415417, 1.7917594692, 2.1972245773, 1.7917594692, 2.0794415417, 1.6094379124, 2.0794415417, 1.7917594692, 2.0794415417, 1.7917594692, 2.0794415417, 1.3862943611, 1.3862943611, 1.6094379124, 2.0794415417, 1.7917594692, more...

decimal, non-constant, non-monotonic, +0

a(n)=ln(τ(ϕ(n)))
ϕ(n)=Euler's totient function
τ(n)=number of divisors of n
n≥1
4 operations
Prime
nϕτl

Sequence l4qqpyzwckzzp

0, 0, 0.8306408779, 0.8306408779, 0.8306408779, 0.8306408779, 0, 0.8306408779, 0, 0.8306408779, 0, 0.8306408779, 0, 0, 0.8306408779, 0.8306408779, 0.8306408779, 0, 0, 0.8306408779, 0, 0, 0, 0.8306408779, 0, 0, 0, 0, 0, 0.8306408779, 0, 0.8306408779, 0, 0.8306408779, 0, 0, 0, 0, 0, 0.8306408779, 0, 0, 0, 0, 0, 0, 0, 0.8306408779, 0, 0, more...

decimal, non-constant, non-monotonic, +0

a(n)=tan(Λ(ϕ(n)))
ϕ(n)=Euler's totient function
Λ(n)=Von Mangoldt's function
n≥1
4 operations
Prime
nϕΛW

Sequence dkppossvv0z5l

0, 0, 0.8306408779, 0.8306408779, 5.3583557768, 0.8306408779, -4.451746403, 5.3583557768, -4.451746403, 5.3583557768, -1.1134071468, 5.3583557768, -0.7708083714, -4.451746403, -1.7934601498, -1.7934601498, -0.3867176888, -4.451746403, -0.2566428249, -1.7934601498, -0.7708083714, -1.1134071468, -0.0505933016, -1.7934601498, -0.1469036648, -0.7708083714, -0.2566428249, -0.7708083714, 0.1929543996, -1.7934601498, 0.2655983419, -0.3867176888, -0.1469036648, -0.3867176888, 0.0364773427, -0.7708083714, 0.4731358818, -0.2566428249, 0.0364773427, -0.3867176888, 0.609378318, -0.7708083714, 0.6783930094, -0.1469036648, 0.0364773427, -0.0505933016, 0.8203865534, -0.3867176888, 0.6783930094, -0.1469036648, more...

decimal, non-constant, non-monotonic, +-0

a(n)=tan(ln(ϕ(n)))
ϕ(n)=Euler's totient function
n≥1
4 operations
Prime
nϕlW

Sequence te1rjolvhemdn

0, 0, 0.8325546112, 0.8325546112, 0.8325546112, 0.8325546112, 0, 0.8325546112, 0, 0.8325546112, 0, 0.8325546112, 0, 0, 0.8325546112, 0.8325546112, 0.8325546112, 0, 0, 0.8325546112, 0, 0, 0, 0.8325546112, 0, 0, 0, 0, 0, 0.8325546112, 0, 0.8325546112, 0, 0.8325546112, 0, 0, 0, 0, 0, 0.8325546112, 0, 0, 0, 0, 0, 0, 0, 0.8325546112, 0, 0, more...

decimal, non-constant, non-monotonic, +0

a(n)=sqrt(Λ(ϕ(n)))
ϕ(n)=Euler's totient function
Λ(n)=Von Mangoldt's function
n≥1
4 operations
Prime
nϕΛQ

Sequence w45cfjegp4tio

0, 0, 0.8325546112, 0.8325546112, 1.1774100225, 0.8325546112, 1.338566199, 1.1774100225, 1.338566199, 1.1774100225, 1.5174271294, 1.1774100225, 1.5763586679, 1.338566199, 1.4420268866, 1.4420268866, 1.6651092223, 1.338566199, 1.700109337, 1.4420268866, 1.5763586679, 1.5174271294, 1.7581360736, 1.4420268866, 1.7308183826, 1.5763586679, 1.700109337, 1.5763586679, 1.8254326912, 1.4420268866, 1.8442335486, 1.6651092223, 1.7308183826, 1.6651092223, 1.7827096876, 1.5763586679, 1.8930184728, 1.700109337, 1.7827096876, 1.6651092223, 1.9206455826, 1.5763586679, 1.9333053608, 1.7308183826, 1.7827096876, 1.7581360736, 1.9566914413, 1.6651092223, 1.9333053608, 1.7308183826, more...

decimal, non-constant, non-monotonic, +0

a(n)=sqrt(ln(ϕ(n)))
ϕ(n)=Euler's totient function
n≥1
4 operations
Prime
nϕlQ

Sequence 5h3iyy0ondiyb

0, 0, 0.8414709848, 0.8414709848, 0.9092974268, 0.8414709848, 0.9092974268, 0.9092974268, 0.9092974268, 0.9092974268, 0.9092974268, 0.9092974268, 0.1411200081, 0.9092974268, 0.1411200081, 0.1411200081, -0.7568024953, 0.9092974268, 0.1411200081, 0.1411200081, 0.1411200081, 0.9092974268, 0.9092974268, 0.1411200081, 0.1411200081, 0.1411200081, 0.1411200081, 0.1411200081, 0.1411200081, 0.1411200081, 0.1411200081, -0.7568024953, 0.1411200081, -0.7568024953, -0.7568024953, 0.1411200081, -0.7568024953, 0.1411200081, -0.7568024953, -0.7568024953, -0.7568024953, 0.1411200081, 0.1411200081, 0.1411200081, -0.7568024953, 0.9092974268, 0.9092974268, -0.7568024953, 0.1411200081, 0.1411200081, more...

decimal, non-constant, non-monotonic, +-0

a(n)=sin(Ω(ϕ(n)))
ϕ(n)=Euler's totient function
Ω(n)=max factorization terms
n≥1
4 operations
Prime
nϕΩS

Sequence hqjeaju55hdj

0, 0, 1, 0, 1, 0, 1, 0, 3, 2, 1, 0, 1, 2, 7, 0, 1, 0, 1, 4, 9, 2, 1, 0, 5, 2, 9, 4, 1, 6, 1, 0, 13, 2, 11, 0, 1, 2, 15, 8, 1, 6, 1, 4, 21, 2, 1, 0, 7, 10, more...

integer, non-constant, non-monotonic, +0, A068494

a(n)=n%ϕ(n)
ϕ(n)=Euler's totient function
n≥1
4 operations
Prime
nnϕ%

Sequence mxmj30h0adkse

0, 0, 1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, -1, 0, 0, -1, 0, -1, 0, 0, 0, -1, -1, -1, 0, -1, -1, 0, -1, -1, more...

integer, non-constant, non-monotonic, +-0

a(n)=μ(Ω(ϕ(n)))
ϕ(n)=Euler's totient function
Ω(n)=max factorization terms
μ(n)=Möbius function
n≥1
4 operations
Prime
nϕΩμ

Sequence e2zrmqrqolo2l

0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, more...

integer, non-constant, non-monotonic, +0

a(n)=ceil(Λ(ϕ(n)))
ϕ(n)=Euler's totient function
Λ(n)=Von Mangoldt's function
n≥1
4 operations
Prime
nϕΛT

Sequence 3mrutkxmdzhxf

0, 0, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 1, 2, 1, 3, 2, 2, 2, 3, 1, 3, 2, 3, 2, 3, 2, 2, 1, 3, 2, more...

integer, non-constant, non-monotonic, +0

a(n)=Ω(τ(ϕ(n)))
ϕ(n)=Euler's totient function
τ(n)=number of divisors of n
Ω(n)=max factorization terms
n≥1
4 operations
Prime
nϕτΩ

Sequence goj2umamw1qho

0, 0, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 2, 2, 2, 3, 2, 3, 2, 2, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 3, 3, 3, 3, 2, 4, 3, 3, 3, 4, 2, 4, 3, 3, 3, 4, 3, 4, 3, more...

integer, non-constant, non-monotonic, +0

a(n)=round(ln(ϕ(n)))
ϕ(n)=Euler's totient function
n≥1
4 operations
Prime
nϕlR

Sequence qlbhzt14qqgyj

0, 0, 1, 1, 1.4142135624, 1, 1.4142135624, 1.4142135624, 1.4142135624, 1.4142135624, 1.4142135624, 1.4142135624, 1.7320508076, 1.4142135624, 1.7320508076, 1.7320508076, 2, 1.4142135624, 1.7320508076, 1.7320508076, 1.7320508076, 1.4142135624, 1.4142135624, 1.7320508076, 1.7320508076, 1.7320508076, 1.7320508076, 1.7320508076, 1.7320508076, 1.7320508076, 1.7320508076, 2, 1.7320508076, 2, 2, 1.7320508076, 2, 1.7320508076, 2, 2, 2, 1.7320508076, 1.7320508076, 1.7320508076, 2, 1.4142135624, 1.4142135624, 2, 1.7320508076, 1.7320508076, more...

decimal, non-constant, non-monotonic, +0

a(n)=sqrt(Ω(ϕ(n)))
ϕ(n)=Euler's totient function
Ω(n)=max factorization terms
n≥1
4 operations
Prime
nϕΩQ

Sequence 2zummjwq1a1eg

0, 0, 1, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 3, 3, 2, 3, 2, 3, 3, 3, 2, 2, 2, 3, 2, 2, 3, 2, 2, more...

integer, non-constant, non-monotonic, +0

a(n)=τ(Ω(ϕ(n)))
ϕ(n)=Euler's totient function
Ω(n)=max factorization terms
τ(n)=number of divisors of n
n≥1
4 operations
Prime
nϕΩτ

Sequence tavqzeyvyi0jh

0, 0, 1, 1, 2, 1, 2, 2, 2, 2, 3, 2, 3, 2, 3, 3, 3, 2, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 4, 3, 4, 3, 3, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 4, 4, 3, 4, 3, more...

integer, non-constant, non-monotonic, +0

a(n)=ceil(ln(ϕ(n)))
ϕ(n)=Euler's totient function
n≥1
4 operations
Prime
nϕlT

Sequence wqcp1gvda4hph

0, 0, 1, 1, 3, 1, 5, 3, 5, 3, 9, 3, 11, 5, 7, 7, 15, 5, 17, 7, 11, 9, 21, 7, 19, 11, 17, 11, 27, 7, 29, 15, 19, 15, 23, 11, 35, 17, 23, 15, 39, 11, 41, 19, 23, 21, 45, 15, 41, 19, more...

integer, non-constant, non-monotonic, +0, A109606

a(n)=ϕ(n)-1
ϕ(n)=Euler's totient function
n≥1
4 operations
Prime
nϕ1-

Sequence gwfdhrtuztuyn

0, 0, 1.5574077247, 1.5574077247, -2.1850398633, 1.5574077247, -2.1850398633, -2.1850398633, -2.1850398633, -2.1850398633, -2.1850398633, -2.1850398633, -0.1425465431, -2.1850398633, -0.1425465431, -0.1425465431, 1.1578212823, -2.1850398633, -0.1425465431, -0.1425465431, -0.1425465431, -2.1850398633, -2.1850398633, -0.1425465431, -0.1425465431, -0.1425465431, -0.1425465431, -0.1425465431, -0.1425465431, -0.1425465431, -0.1425465431, 1.1578212823, -0.1425465431, 1.1578212823, 1.1578212823, -0.1425465431, 1.1578212823, -0.1425465431, 1.1578212823, 1.1578212823, 1.1578212823, -0.1425465431, -0.1425465431, -0.1425465431, 1.1578212823, -2.1850398633, -2.1850398633, 1.1578212823, -0.1425465431, -0.1425465431, more...

decimal, non-constant, non-monotonic, +-0

a(n)=tan(Ω(ϕ(n)))
ϕ(n)=Euler's totient function
Ω(n)=max factorization terms
n≥1
4 operations
Prime
nϕΩW

Sequence ifhn4ckgj0eyk

0, 0.8414709848, 0.8414709848, 0.8414709848, 0.8414709848, 0.8414709848, 0.8414709848, 0.9092974268, 0.8414709848, 0.8414709848, 0.8414709848, 0.9092974268, 0.8414709848, 0.8414709848, 0.8414709848, 0.9092974268, 0.8414709848, 0.9092974268, 0.8414709848, 0.9092974268, 0.8414709848, 0.8414709848, 0.8414709848, 0.9092974268, 0.8414709848, 0.8414709848, 0.9092974268, 0.9092974268, 0.8414709848, 0.9092974268, 0.8414709848, -0.7568024953, 0.8414709848, 0.8414709848, 0.8414709848, 0.9092974268, 0.8414709848, 0.8414709848, 0.8414709848, 0.9092974268, 0.8414709848, 0.9092974268, 0.8414709848, 0.9092974268, 0.9092974268, 0.8414709848, 0.8414709848, -0.7568024953, 0.8414709848, 0.9092974268, more...

decimal, non-constant, non-monotonic, +-0

a(n)=sin(ϕ(Ω(n)))
Ω(n)=max factorization terms
ϕ(n)=Euler's totient function
n≥1
4 operations
Prime
nΩϕS

Sequence m4bhccxqyktgi

0, 1, 0, 2, 0, 4, -2, 8, -4, 10, -6, 16, -12, 24, -18, 26, -18, 34, -28, 46, -38, 50, -40, 62, -54, 74, -62, 80, -68, 96, -88, 118, -102, 122, -106, 130, -118, 154, -136, 160, -144, 184, -172, 214, -194, 218, -196, 242, -226, 268, more...

integer, non-constant, non-monotonic, +-0

a(n)=ϕ(n)-a(n-1)
a(0)=0
ϕ(n)=Euler's totient function
n≥0
4 operations
PrimeRecursive
nϕr-

Sequence yxw01i4f4zcth

0, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1, -1, 1, 1, 1, -1, 1, 1, -1, -1, 1, -1, 1, 0, 1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1, -1, -1, 1, 1, 0, 1, -1, more...

integer, non-constant, non-monotonic, +-0

a(n)=μ(ϕ(Ω(n)))
Ω(n)=max factorization terms
ϕ(n)=Euler's totient function
μ(n)=Möbius function
n≥1
4 operations
Prime
nΩϕμ

Sequence mnuuosdbnlttm

0, 1, 1, 1, 1, 1, 1, 1.4142135624, 1, 1, 1, 1.4142135624, 1, 1, 1, 1.4142135624, 1, 1.4142135624, 1, 1.4142135624, 1, 1, 1, 1.4142135624, 1, 1, 1.4142135624, 1.4142135624, 1, 1.4142135624, 1, 2, 1, 1, 1, 1.4142135624, 1, 1, 1, 1.4142135624, 1, 1.4142135624, 1, 1.4142135624, 1.4142135624, 1, 1, 2, 1, 1.4142135624, more...

decimal, non-constant, non-monotonic, +0

a(n)=sqrt(ϕ(Ω(n)))
Ω(n)=max factorization terms
ϕ(n)=Euler's totient function
n≥1
4 operations
Prime
nΩϕQ

Sequence e0d3joj0uqtvm

0, 1, 1, 1, 2, 2, 2, 4, 2, 6, 2, 6, 2, 10, 2, 12, 2, 8, 4, 8, 4, 16, 2, 12, 4, 12, 6, 12, 8, 12, 6, 20, 4, 28, 2, 20, 8, 28, 4, 24, 8, 20, 10, 20, 8, 36, 4, 42, 2, 46, more...

integer, non-constant, non-monotonic, +0

a(n)=ϕ(n-a(n-1))
a(0)=0
ϕ(n)=Euler's totient function
n≥0
4 operations
PrimeRecursive
nr-ϕ

Sequence qzhxj2jtgpnf

0, 1, 1, 2, 1, 4, 1, 4, 3, 6, 1, 8, 1, 8, 7, 8, 1, 12, 1, 12, 9, 12, 1, 16, 5, 14, 9, 16, 1, 22, 1, 16, 13, 18, 11, 24, 1, 20, 15, 24, 1, 30, 1, 24, 21, 24, 1, 32, 7, 30, more...

integer, non-constant, non-monotonic, +0, A051953

a(n)=n-ϕ(n)
ϕ(n)=Euler's totient function
n≥1
4 operations
Prime
nnϕ-

Sequence hzzniwrvc0yqf

0, 1, 1, 2, 2, 3, 4, 5, 8, 9, 14, 15, 22, 25, 42, 37, 78, 61, 138, 105, 186, 165, 266, 273, 410, 433, 842, 853, 1694, 1513, 3102, 2433, 4722, 4005, 6834, 6117, 10910, more...

integer, non-constant, non-monotonic, +0

a(n)=ϕ(a(n-1))+a(n-2)
a(0)=0
a(1)=1
ϕ(n)=Euler's totient function
n≥0
4 operations
PrimeRecursive
rϕs+

Sequence sjuck01osm4vh

0, 1, 1, 2, 2, 4, 2, 6, 4, 6, 4, 10, 4, 12, 6, 8, 8, 16, 6, 18, 8, 12, 10, 22, 8, 20, 12, 18, 12, 28, 8, 30, 16, 20, 16, 24, 12, 36, 18, 24, 16, 40, 12, 42, 20, 24, 22, 46, 16, 42, more...

integer, non-constant, non-monotonic, +0

a(n)=ϕ(n-1)
ϕ(n)=Euler's totient function
n≥1
4 operations
Prime
n1-ϕ

Sequence pmru5d4rcvycj

0, 1, 1, 2, 3, 3, 4, 5, 4, 7, 4, 9, 6, 11, 4, 13, 4, 15, 10, 15, 12, 17, 6, 21, 12, 21, 14, 21, 16, 21, 18, 25, 12, 29, 6, 33, 16, 29, 10, 35, 16, 33, 22, 33, 24, 37, 10, 43, 6, 47, more...

integer, non-constant, non-monotonic, +0

a(n)=n-ϕ(a(n-1))
a(0)=0
ϕ(n)=Euler's totient function
n≥0
4 operations
PrimeRecursive
nrϕ-

Sequence 31f5zrotzls2k

0, 1, 1, 2, 3, 4, 6, 8, 10, 14, 18, 24, 30, 38, 46, 64, 86, 118, 160, 218, 282, 390, 482, 578, 818, 1090, 1498, 1930, 2566, 3334, 4616, 6282, 8586, 10674, 13482, more...

integer, non-constant, monotonic, +0

a(n)=a(n-1)+ϕ(a(n-2))
a(0)=0
a(1)=1
ϕ(n)=Euler's totient function
n≥0
4 operations
PrimeRecursive
rsϕ+

Sequence lmqnqwsfq0wgm

0, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, more...

integer, non-constant, monotonic, +0, A130130

a(n)=ceil(sqrt(ln(n)))
n≥1
4 operations
N
nlQT
a(n)=floor(sqrt(a(n-1)))+1
a(0)=0
n≥0
5 operations
Recursive
rQf1+
a(n)=ϕ(a(n-1))+1
a(0)=0
ϕ(n)=Euler's totient function
n≥0
4 operations
PrimeRecursive
rϕ1+

Sequence a1teiwyikqael

0, 1, 2, 2, 4, 2, 6, 4, 6, 4, 10, 4, 12, 6, 8, 8, 16, 6, 18, 8, 12, 10, 22, 8, 20, 12, 18, 12, 28, 8, 30, 16, 20, 16, 24, 12, 36, 18, 24, 16, 40, 12, 42, 20, 24, 22, 46, 16, 42, 20, more...

integer, non-constant, non-monotonic, +0

a(n)=ϕ(n)%n
ϕ(n)=Euler's totient function
n≥1
4 operations
Prime
nϕn%