Sequence Database

A database with 1956199 machine generated integer and decimal sequences.

Displaying result 0-99 of total 1148. [0] [1] [2] [3] [4] ... [11]

Sequence jr31e1aueykgh

5, 25, 625, 390625, 152587890625, more...

integer, strictly-monotonic, +, A176594 (multiple)

a(n)=a(n-1)²
a(0)=5
n≥0
2 operations
Recursive

Sequence e4emqpwkajic

0, 1, 3, 1, 4, 1, 3, 3, 200, 1, 3, 1, 10, 33, 1, 1, 2, 20, 5, 3, 4, 5, 2, 5, 1, 3, 1, 2, 3, 1, 71, 2, 1, 2, 3, 67, 1, 1, 2, 5, 1, 1, 3, 1, 7, 4, 14, 1, 1, 2, more...

integer, non-monotonic, +, A119719 (weak, multiple)

a(n)=contfrac[log2(γ)]
γ=0.5772... (Euler Gamma)
contfrac(a)=continued fraction of a
n≥0
3 operations
Power

Sequence zbmpekmlvbqz

0, 47, 94, 141, 188, 235, 282, 329, 376, 423, 470, 517, 564, 611, 658, 705, 752, 799, 846, 893, 940, 987, 1034, 1081, 1128, 1175, 1222, 1269, 1316, 1363, 1410, 1457, 1504, 1551, 1598, 1645, 1692, 1739, 1786, 1833, 1880, 1927, 1974, 2021, 2068, 2115, 2162, 47, 2256, 2303, more...

integer, non-monotonic, +, A004963 (multiple)

a(n)=lcm(n, 47)
lcm(a,b)=least common multiple
n≥0
3 operations
Divisibility

Sequence hs40dge3brqyj

0, 47, 94, 141, 188, 235, 282, 329, 376, 423, 470, 517, 564, 611, 658, 705, 752, 799, 846, 893, 940, 987, 1034, 1081, 1128, 1175, 1222, 1269, 1316, 1363, 1410, 1457, 1504, 1551, 1598, 1645, 1692, 1739, 1786, 1833, 1880, 1927, 1974, 2021, 2068, 2115, 2162, 2209, 2256, 2303, more...

integer, strictly-monotonic, +, A004963 (multiple)

a(n)=47*n
n≥0
3 operations
Arithmetic

Sequence b21dwzgd2akbp

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

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=μ(P(n))
P(n)=partition numbers
μ(n)=Möbius function
n≥0
3 operations
Prime

Sequence k0jf0mc4r4kwf

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-monotonic, +-, A071759 (weak, multiple)

a(n)=λ(P(n))
P(n)=partition numbers
λ(n)=Liouville's function
n≥0
3 operations
Prime

Sequence rjjphoxgo2rve

1, 1, 1, 4, 10, 1, 1, 128, 1, 10, 1, 1, 5, 16, 1, 2, 34, 1, 15, 3, 1, 4, 1, 3, 1, 1, 11, 1, 6, 1, 4, 2, 7, 3, 27, 3, 19, 11, 1, 1, 1, 1, 14, 1, 21, 1, 1, 4, 1, 7, more...

integer, non-monotonic, +, A276272 (weak, multiple)

a(n)=contfrac[atan(61)]
contfrac(a)=continued fraction of a
n≥0
3 operations
Trigonometric

Sequence kmjchbq0ismd

1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912, 1073741824, 2147483648, 4294967296, 8589934592, 17179869184, 34359738368, 68719476736, 137438953472, 274877906944, 549755813888, 1099511627776, 2199023255552, 4398046511104, 8796093022208, 17592186044416, 35184372088832, 70368744177664, 140737488355328, 281474976710656, 562949953421312, more...

integer, strictly-monotonic, +, A000079 (multiple)

a(n)=2^n
n≥0
3 operations
Power
a(n)=2*a(n-1)
a(0)=1
n≥0
3 operations
Recursive
a(n)=lcm(2*a(n-1), 2)
a(0)=1
lcm(a,b)=least common multiple
n≥0
5 operations
Recursive
a(n)=2*a(n-2)+a(n-1)
a(0)=1
a(1)=2
n≥0
5 operations
Recursive
a(n)=xor(3*a(n-1), a(n-1))
a(0)=1
xor(a,b)=bitwise exclusive or
n≥0
5 operations
Recursive

Sequence lcjxinejhrj5l

1, 2, 6, 12, 60, 120, 840, 1680, 5040, 10080, 110880, 221760, 2882880, 5765760, 17297280, 34594560, 588107520, 1176215040, 22348085760, 44696171520, 134088514560, 268177029120, 6168071669760, 12336143339520, 61680716697600, 123361433395200, 370084300185600, 740168600371200, more...

integer, strictly-monotonic, +, A072486 (multiple)

a(n)=∏[lpf(n)]
lpf(n)=least prime factor of n
∏(a)=partial products of a
n≥1
3 operations
Prime
a(n)=∏[gcd(n, lpf(n))]
lpf(n)=least prime factor of n
gcd(a,b)=greatest common divisor
∏(a)=partial products of a
n≥1
5 operations
Prime
a(n)=∏[gpf(lpf(n)²)]
lpf(n)=least prime factor of n
gpf(n)=greatest prime factor of n
∏(a)=partial products of a
n≥1
5 operations
Prime
a(n)=∏[rad(lpf(n)²)]
lpf(n)=least prime factor of n
rad(n)=square free kernel of n
∏(a)=partial products of a
n≥1
5 operations
Prime
a(n)=∏[exp(Λ(lpf(n)))]
lpf(n)=least prime factor of n
Λ(n)=Von Mangoldt's function
∏(a)=partial products of a
n≥1
5 operations
Prime

Sequence x1hlaoxf5mj4p

1, 2, 6, 12, 60, 360, 2520, 5040, 15120, 151200, 1663200, 9979200, 129729600, 1816214400, 27243216000, 54486432000, 926269344000, 5557616064000, 105594705216000, 1055947052160000, more...

integer, strictly-monotonic, +, A072938 (multiple)

a(n)=∏[rad(n)]
rad(n)=square free kernel of n
∏(a)=partial products of a
n≥1
3 operations
Prime
a(n)=∏[gcd(n, rad(n))]
rad(n)=square free kernel of n
gcd(a,b)=greatest common divisor
∏(a)=partial products of a
n≥1
5 operations
Prime

Sequence pscflvcp500s

1, 4, 16, 64, 256, 1024, 4096, 16384, 65536, 262144, 1048576, 4194304, 16777216, 67108864, 268435456, 1073741824, 4294967296, 17179869184, 68719476736, 274877906944, 1099511627776, 4398046511104, 17592186044416, 70368744177664, 281474976710656, 1125899906842624, more...

integer, strictly-monotonic, +, A000302 (multiple)

a(n)=4^n
n≥0
3 operations
Power
a(n)=4*a(n-1)
a(0)=1
n≥0
3 operations
Recursive
a(n)=lcm(4*a(n-1), 2)
a(0)=1
lcm(a,b)=least common multiple
n≥0
5 operations
Recursive
a(n)=xor(5*a(n-1), a(n-1))
a(0)=1
xor(a,b)=bitwise exclusive or
n≥0
5 operations
Recursive
a(n)=Δ[a(n-1)²/a(n-2)]²
a(0)=1
a(1)=2
Δ(a)=differences of a
n≥0
6 operations
Recursive

Sequence ajhxlmhyo3n5e

1, 10, 45, 120, 210, 252, 210, 120, 45, 10, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, more...

integer, non-monotonic, +, A010926 (weak, multiple)

a(n)=C(10, n)
C(n,k)=binomial coefficient
n≥0
3 operations
Combinatoric

Sequence yo2k1d13q4dpc

1, 24, 720, 40320, 362880, 3628800, 479001600, 87178291200, 1307674368000, 20922789888000, more...

integer, strictly-monotonic, +, A062313 (multiple)

a(n)=composite(n)!
composite(n)=nth composite number
n≥1
3 operations
Prime
a(n)=comp[gpf(n)]!
gpf(n)=greatest prime factor of n
comp(a)=complement function of a (in range)
n≥1
4 operations
Prime
a(n)=comp[lpf(n)]!
lpf(n)=least prime factor of n
comp(a)=complement function of a (in range)
n≥1
4 operations
Prime
a(n)=comp[exp(Λ(n))]!
Λ(n)=Von Mangoldt's function
comp(a)=complement function of a (in range)
n≥1
5 operations
Prime

Sequence dll4il3gfpetp

2, 2, 4, 16, 4294967296, more...

integer, monotonic, +, A079556 (weak, multiple)

a(n)=a(n-2)^a(n-1)
a(0)=2
a(1)=2
n≥0
3 operations
Recursive

Sequence 1rlucwpmwfwnf

3, 6, 12, 48, 768, more...

integer, strictly-monotonic, +, A085866 (multiple)

a(n)=φ(a(n-1)²)
a(0)=3
ϕ(n)=number of relative primes (Euler's totient)
n≥0
3 operations
Prime

Sequence nnasoawu1p4eb

4, 9, 25, 49, 121, 169, 289, 361, 529, 841, 961, 1369, 1681, 1849, 2209, 2809, 3481, 3721, 4489, 5041, 5329, 6241, 6889, 7921, 9409, 10201, 10609, 11449, 11881, 12769, 16129, 17161, 18769, 19321, 22201, 22801, 24649, 26569, 27889, 29929, 32041, 32761, 36481, 37249, 38809, 39601, 44521, 49729, 51529, 52441, more...

integer, strictly-monotonic, +, A001248 (multiple)

a(n)=p(n)²
p(n)=nth prime
n≥1
3 operations
Prime
a(n)=root(1/2, p(n))
p(n)=nth prime
root(n,a)=the n-th root of a
n≥1
6 operations
Prime
a(n)=exp(2*log(p(n)))
p(n)=nth prime
n≥1
6 operations
Prime

Sequence pdebowjm4goyj

5, 7, 13, 37, 151, 863, 6689, 67139, more...

integer, strictly-monotonic, +, A064600 (multiple)

a(n)=p(φ(a(n-1)))
a(0)=5
ϕ(n)=number of relative primes (Euler's totient)
p(n)=nth prime
n≥0
3 operations
Prime

Sequence 2fibat0u3gscf

48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 0, 1, more...

integer, non-monotonic, +, A121377 (multiple)

a(n)=xor(48, n)
xor(a,b)=bitwise exclusive or
n≥0
3 operations
Bitwise

Sequence f5doav4wydkhi

48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 48, 49, more...

integer, periodic-16, non-monotonic, +, A121377 (multiple)

a(n)=or(48, n)
or(a,b)=bitwise or
n≥0
3 operations
Bitwise

Sequence twxqqtb3re54e

48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, more...

integer, strictly-monotonic, +, A121377 (multiple)

a(n)=48+n
n≥0
3 operations
Arithmetic

Sequence 5bojem4eilhmo

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

integer, non-monotonic, +-, A172565 (weak, multiple)

a(n)=Δ[agc(agc(n))]
agc(n)=number of factorizations into prime powers (abelian group count)
Δ(a)=differences of a
n≥0
4 operations
Prime
a(n)=Δ[P(agc(agc(n)))]
agc(n)=number of factorizations into prime powers (abelian group count)
P(n)=partition numbers
Δ(a)=differences of a
n≥0
5 operations
Prime
a(n)=Δ[gpf(agc(agc(n)))]
agc(n)=number of factorizations into prime powers (abelian group count)
gpf(n)=greatest prime factor of n
Δ(a)=differences of a
n≥0
5 operations
Prime
a(n)=Δ[lpf(agc(agc(n)))]
agc(n)=number of factorizations into prime powers (abelian group count)
lpf(n)=least prime factor of n
Δ(a)=differences of a
n≥0
5 operations
Prime
a(n)=Δ[rad(agc(agc(n)))]
agc(n)=number of factorizations into prime powers (abelian group count)
rad(n)=square free kernel of n
Δ(a)=differences of a
n≥0
5 operations
Prime

Sequence wj010irzpbyrb

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

integer, non-monotonic, +-, A172565 (weak, multiple)

a(n)=Δ[agc(n²)]
agc(n)=number of factorizations into prime powers (abelian group count)
Δ(a)=differences of a
n≥0
4 operations
Prime
a(n)=Δ[log2(agc(n²))]
agc(n)=number of factorizations into prime powers (abelian group count)
Δ(a)=differences of a
n≥0
5 operations
Prime
a(n)=Δ[P(agc(n²))]
agc(n)=number of factorizations into prime powers (abelian group count)
P(n)=partition numbers
Δ(a)=differences of a
n≥0
5 operations
Prime
a(n)=Δ[catalan(agc(n²))]
agc(n)=number of factorizations into prime powers (abelian group count)
catalan(n)=the catalan numbers
Δ(a)=differences of a
n≥0
5 operations
Prime
a(n)=Δ[p(agc(n²))]
agc(n)=number of factorizations into prime powers (abelian group count)
p(n)=nth prime
Δ(a)=differences of a
n≥0
5 operations
Prime

Sequence 4o4tvnydtht1h

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

integer, non-monotonic, +-, A172565 (weak, multiple)

a(n)=Δ[stern(agc(n))]
agc(n)=number of factorizations into prime powers (abelian group count)
stern(n)=Stern-Brocot sequence
Δ(a)=differences of a
n≥0
4 operations
Prime
a(n)=Δ[P(stern(agc(n)))]
agc(n)=number of factorizations into prime powers (abelian group count)
stern(n)=Stern-Brocot sequence
P(n)=partition numbers
Δ(a)=differences of a
n≥0
5 operations
Prime
a(n)=Δ[gpf(stern(agc(n)))]
agc(n)=number of factorizations into prime powers (abelian group count)
stern(n)=Stern-Brocot sequence
gpf(n)=greatest prime factor of n
Δ(a)=differences of a
n≥0
5 operations
Prime
a(n)=Δ[lpf(stern(agc(n)))]
agc(n)=number of factorizations into prime powers (abelian group count)
stern(n)=Stern-Brocot sequence
lpf(n)=least prime factor of n
Δ(a)=differences of a
n≥0
5 operations
Prime
a(n)=Δ[rad(stern(agc(n)))]
agc(n)=number of factorizations into prime powers (abelian group count)
stern(n)=Stern-Brocot sequence
rad(n)=square free kernel of n
Δ(a)=differences of a
n≥0
5 operations
Prime

Sequence ak1t2ywkh4rjd

0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 3, -3, 0, 0, 0, 0, 0, 0, 1, -1, 0, 1, -1, 0, 0, 0, 5, -5, 0, 0, 1, -1, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 3, -3, 0, 0, more...

integer, non-monotonic, +-, A172565 (weak, multiple)

a(n)=Δ[φ(agc(n))]
agc(n)=number of factorizations into prime powers (abelian group count)
ϕ(n)=number of relative primes (Euler's totient)
Δ(a)=differences of a
n≥0
4 operations
Prime

Sequence zlgwij3gjyaf

0, 1, 3, 4, 6, 7, 9, 10, 11, 13, 14, 16, 17, 19, 20, 22, 23, 24, 26, 27, 29, 30, 32, 33, 35, 36, 37, 39, 40, 42, 43, 45, 46, 48, 49, 50, more...

integer, strictly-monotonic, +, A275672 (weak, multiple)

a(n)=floor(log2(sinh(n)))
n≥1
4 operations
Trigonometric

Sequence c03lbpe00my1

0, 1, 3, 6, 11, 16, 22, 29, 36, 44, 54, 63, 74, 85, 96, 109, 121, 135, 149, 164, 179, 195, 211, 228, 246, 264, 282, 301, 321, 341, 362, 383, 405, 427, 450, 473, 496, 521, 545, 570, 596, 622, 648, 675, 703, 731, 759, 788, 817, 847, more...

integer, strictly-monotonic, +, A181947 (weak, multiple)

a(n)=floor(root(γ, n))
γ=0.5772... (Euler Gamma)
root(n,a)=the n-th root of a
n≥0
4 operations
Power

Sequence ydebondwjz52p

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

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=μ(floor(log2(n)))
μ(n)=Möbius function
n≥2
4 operations
Prime

Sequence p1skl520y3o4o

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-monotonic, +-, A071759 (weak, multiple)

a(n)=λ(σ(φ(n)))
ϕ(n)=number of relative primes (Euler's totient)
σ(n)=divisor sum of n
λ(n)=Liouville's function
n≥1
4 operations
Prime

Sequence 2lauifrshh1ye

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-monotonic, +-, A071759 (weak, multiple)

a(n)=λ(floor(log2(n)))
λ(n)=Liouville's function
n≥2
4 operations
Prime

Sequence q5o2yw32qmg1d

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

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=μ(round(sqrt(n)))
μ(n)=Möbius function
n≥1
4 operations
Prime

Sequence dnlm2g0h2avo

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

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=μ(P(φ(n)))
ϕ(n)=number of relative primes (Euler's totient)
P(n)=partition numbers
μ(n)=Möbius function
n≥1
4 operations
Prime

Sequence bpdwob1gljssm

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-monotonic, +-, A071759 (weak, multiple)

a(n)=λ(P(φ(n)))
ϕ(n)=number of relative primes (Euler's totient)
P(n)=partition numbers
λ(n)=Liouville's function
n≥1
4 operations
Prime

Sequence 3hpcoptbpb5jm

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-monotonic, +-, A071759 (weak, multiple)

a(n)=λ(round(sqrt(n)))
λ(n)=Liouville's function
n≥1
4 operations
Prime

Sequence friszl5zqq20

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

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=μ(Ω(∑[n]))
∑(a)=partial sums of a
Ω(n)=number of prime divisors of n
μ(n)=Möbius function
n≥2
4 operations
Prime

Sequence ndutrh0t3v15k

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

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=μ(or(1, n))
or(a,b)=bitwise or
μ(n)=Möbius function
n≥0
4 operations
Prime

Sequence me5fmgj0nnige

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-monotonic, +-, A071759 (weak, multiple)

a(n)=λ(Ω(∑[n]))
∑(a)=partial sums of a
Ω(n)=number of prime divisors of n
λ(n)=Liouville's function
n≥2
4 operations
Prime

Sequence xz5dloz3ctp2d

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-monotonic, +-, A071759 (weak, multiple)

a(n)=λ(or(1, n))
or(a,b)=bitwise or
λ(n)=Liouville's function
n≥0
4 operations
Prime

Sequence leuxnovwnbo4n

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

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=μ(τ(P(n)))
P(n)=partition numbers
τ(n)=number of divisors of n
μ(n)=Möbius function
n≥0
4 operations
Prime

Sequence o0litp05zkxki

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-monotonic, +-, A071759 (weak, multiple)

a(n)=λ(τ(P(n)))
P(n)=partition numbers
τ(n)=number of divisors of n
λ(n)=Liouville's function
n≥0
4 operations
Prime

Sequence 2sfmlcocvffnc

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-monotonic, +-, A071759 (weak, multiple)

a(n)=μ(rad(P(n)))
P(n)=partition numbers
rad(n)=square free kernel of n
μ(n)=Möbius function
n≥0
4 operations
Prime
a(n)=λ(rad(P(n)))
P(n)=partition numbers
rad(n)=square free kernel of n
λ(n)=Liouville's function
n≥0
4 operations
Prime

Sequence yrgje2sbgkvsn

1, 1, 1, 1, 1, 3, 4, 1, 1, 1, 1, 1, 3, 286, 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-monotonic, +, A171604 (weak, multiple)

a(n)=pt(lpf(P(n)))
P(n)=partition numbers
lpf(n)=least prime factor of n
pt(n)=Pascals triangle by rows
n≥0
4 operations
Prime

Sequence q50o1kjpujrfh

1, 1, 1, 6, 4, 1, 7, 1, 8, 4, 1, 1, 10, 1, 1, 1, 12, 15, 1, 29, 1, 2, 2, 26, 4, 1, 1, 5, 3, 1, 1, 5, 7, 1, 1, 1, 1, 40, 11, 1, 3, 1, 2, 4, 10, 1, 1, 13, 7, 72, more...

integer, non-monotonic, +, A081538 (weak, multiple)

a(n)=contfrac[cosh(tanh(3))]
contfrac(a)=continued fraction of a
n≥0
4 operations
Trigonometric

Sequence aq5yo4tvghidg

1, 1, 2, 2, 5, 6, 1, 2, 9, 7, 8, 2, 3, 1, 3, 9, 7, 8, 3, 8, 0, 5, 8, 1, 0, 8, 6, 7, 6, 3, 5, 8, 4, 5, 2, 0, 3, 0, 5, 7, 4, 1, 9, 6, 2, 2, 9, 7, 0, 4, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=de[cosh(cot(68))]
de(a)=decimal expansion of a
n≥0
4 operations
Trigonometric

Sequence kzqkahqfvx5ch

1, 1, 2, 2, 5, 6, 3, 4, 5, 6, 3, 6, 1, 1, 3, 4, 1, 7, 6, 6, 9, 9, 0, 5, 5, 3, 0, 2, 0, 7, 3, 1, 3, 2, 7, 3, 4, 5, 4, 7, 7, 2, 9, 8, 9, 1, 3, 7, 7, 4, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=de[root(25, 18)]
root(n,a)=the n-th root of a
de(a)=decimal expansion of a
n≥0
4 operations
Power

Sequence l0tbwuqihwsel

1, 1, 4, 16, 64, 256, 900, 3600, 9216, more...

integer, monotonic, +, A265032 (weak, multiple)

a(n)=τ(n!)²
τ(n)=number of divisors of n
n≥0
4 operations
Prime

Sequence vudrp3lsuejcp

1, 2, 3, 4, 4, 5, 6, 6, 7, 7, 8, 8, 8, 9, 9, 10, 10, 10, 11, 11, 11, 12, 12, 12, 13, 13, 13, 14, 14, 14, 15, 15, 15, 15, 16, 16, 16, 17, 17, 17, 17, 18, 18, 18, 18, 19, 19, 19, 19, 20, more...

integer, monotonic, +, A187103 (weak, multiple)

a(n)=ceil(∑[sin(a(n-1))])
a(0)=1
∑(a)=partial sums of a
n≥0
4 operations
Trigonometric

Sequence 2ujqdclsceafp

1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 13, 14, 16, 17, 18, 19, 21, 22, 23, 24, 26, 27, 28, 29, 31, 32, 33, 34, 36, 37, 38, 39, 41, 42, 43, 44, 46, 47, 48, 49, more...

integer, strictly-monotonic, +, A039116 (multiple)

a(n)=comp[5*n]
comp(a)=complement function of a (in range)
n≥0
4 operations
Arithmetic
a(n)=comp[lcm(n, 5)]
lcm(a,b)=least common multiple
comp(a)=complement function of a (in range)
n≥0
4 operations
Divisibility
a(n)=comp[5+a(n-1)]
a(0)=0
comp(a)=complement function of a (in range)
n≥0
4 operations
Recursive
a(n)=comp[5*stern(n)]
stern(n)=Stern-Brocot sequence
comp(a)=complement function of a (in range)
n≥0
5 operations
Recursive
a(n)=comp[∑[xor(5, a(n-1))]]
a(0)=0
xor(a,b)=bitwise exclusive or
∑(a)=partial sums of a
comp(a)=complement function of a (in range)
n≥0
5 operations
Recursive

Sequence g400srlvt5zld

1, 2, 3, 5, 7, 11, 23, 59, 95, more...

integer, strictly-monotonic, +, A048278 (weak, multiple)

a(n)=∑[stern(n!)]
stern(n)=Stern-Brocot sequence
∑(a)=partial sums of a
n≥0
4 operations
Combinatoric
a(n)=stern(n!)+a(n-1)
a(0)=1
stern(n)=Stern-Brocot sequence
n≥0
5 operations
Combinatoric

Sequence ncy5gifgw3gxe

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

integer, strictly-monotonic, +, A177771 (multiple)

a(n)=∑[φ(n)]!
ϕ(n)=number of relative primes (Euler's totient)
∑(a)=partial sums of a
n≥1
4 operations
Prime

Sequence 4kw1lifhiu4vn

1, 2, 24, 720, 3628800, 479001600, 20922789888000, more...

integer, strictly-monotonic, +, A177771 (multiple)

a(n)=φ(p(n))!
p(n)=nth prime
ϕ(n)=number of relative primes (Euler's totient)
n≥1
4 operations
Prime

Sequence jrph2uqez1cl

1, 3, 0, 1, 7, 6, 0, 3, 3, 6, 0, 4, 6, 0, 1, 5, 0, 9, 9, 8, 7, 6, 1, 5, 6, 2, 6, 3, 3, 6, 5, 7, 1, 1, 2, 8, 8, 5, 5, 6, 0, 7, 7, 9, 7, 0, 7, 1, 8, 9, more...

integer, non-monotonic, +, A273155 (weak, multiple)

a(n)=de[atan(sinh(2))]
de(a)=decimal expansion of a
n≥0
4 operations
Trigonometric
a(n)=de[asin(tanh(2))]
de(a)=decimal expansion of a
n≥0
4 operations
Trigonometric

Sequence hyvwbfbxnc5id

1, 3, 0, 1, 7, 6, 2, 6, 5, 1, 1, 3, 5, 2, 9, 7, 9, 6, 2, 7, 2, 4, 1, 4, 3, 5, 5, 5, 1, 3, 4, 3, 7, 0, 7, 1, 2, 7, 6, 9, 3, 8, 6, 5, 7, 2, 3, 0, 3, 3, more...

integer, non-monotonic, +, A273155 (weak, multiple)

a(n)=de[root(16, 68)]
root(n,a)=the n-th root of a
de(a)=decimal expansion of a
n≥0
4 operations
Power

Sequence kknivue30xz5p

1, 3, 0, 1, 7, 6, 5, 9, 1, 7, 9, 1, 1, 1, 9, 2, 6, 7, 5, 4, 1, 3, 2, 0, 1, 2, 0, 1, 4, 0, 3, 8, 5, 4, 5, 2, 7, 4, 8, 2, 5, 4, 9, 2, 1, 6, 4, 7, 7, 1, more...

integer, non-monotonic, +, A273155 (weak, multiple)

a(n)=de[tan(cosh(35))]
de(a)=decimal expansion of a
n≥0
4 operations
Trigonometric

Sequence 0qbgtnkjdvkdk

1, 3, 0, 1, 7, 6, 5, 9, 1, 7, 9, 1, 1, 2, 0, 3, 4, 2, 3, 0, 8, 0, 5, 8, 4, 1, 5, 3, 2, 0, 4, 2, 9, 5, 9, 3, 9, 4, 0, 8, 2, 5, 4, 3, 5, 7, 1, 0, 9, 1, more...

integer, non-monotonic, +, A273155 (weak, multiple)

a(n)=de[tan(sinh(35))]
de(a)=decimal expansion of a
n≥0
4 operations
Trigonometric

Sequence y5y4vr3sgc5jo

1, 3, 3, 4, 5, 2, 0, 5, 9, 9, 2, 1, 4, 9, 4, 6, 6, 2, 2, 3, 3, 5, 6, 4, 4, 0, 9, 4, 8, 8, 8, 0, 9, 3, 4, 4, 1, 4, 3, 8, 8, 8, 3, 3, 7, 7, 5, 3, 1, 7, more...

integer, non-monotonic, +, A003860 (weak, multiple)

a(n)=de[76^QR]
QR=1.6616... (Quadratic Recurrence)
de(a)=decimal expansion of a
n≥0
4 operations
Power

Sequence mrfdagnaqyh1p

1, 4, 3, 4, 5, 6, 1, 7, 1, 9, 9, 4, 6, 7, 4, 2, 7, 5, 8, 9, 4, 8, 7, 1, 9, 8, 8, 5, 0, 3, 5, 0, 1, 9, 8, 1, 9, 6, 7, 7, 4, 4, 6, 1, 8, 2, 6, 6, 1, 2, more...

integer, non-monotonic, +, A132293 (weak, multiple)

a(n)=de[sinh(asin(G))]
G=0.9159... (Catalans)
de(a)=decimal expansion of a
n≥0
4 operations
Trigonometric

Sequence tvzfoqoynpjse

2, 0, 8, 3, 6, 3, 3, 2, 8, 5, 5, 5, 7, 0, 9, 3, 2, 5, 1, 0, 5, 1, 0, 2, 6, 4, 8, 2, 9, 8, 2, 4, 8, 2, 2, 0, 0, 5, 2, 5, 3, 6, 5, 7, 5, 5, 7, 4, 8, 4, more...

integer, non-monotonic, +, A252852 (weak, multiple)

a(n)=de[acos(tan(Khintchine))]
Khintchine=2.6854... (Khintchine)
de(a)=decimal expansion of a
n≥0
4 operations
Trigonometric

Sequence 1qoigg0gj14wn

2, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, more...

integer, monotonic, +, A202102 (weak, multiple)

a(n)=n*lpf(a(n-1))
a(0)=2
lpf(n)=least prime factor of n
n≥0
4 operations
Prime

Sequence vslafn5rcyjqk

2, 6, 1, 2, 2, 18, 1, 16, 11, 1, 1, 1, 1, 4, 6, 4, 2, 79, 1, 1, 5, 3, 34, 3, 377, 1, 3, 1, 180, 76, 1, 2, 3, 1, 31, 7, 2, 1, 7, 1, 1, 1, 1, 2, 11, 2, 4, 2, 1, 1, more...

integer, non-monotonic, +, A246505 (weak, multiple)

a(n)=contfrac[root(e, 8)]
e=2.7182... (Euler e)
root(n,a)=the n-th root of a
contfrac(a)=continued fraction of a
n≥0
4 operations
Power

Sequence d5bw43rd0mj2g

2, 6, 14, 30, 62, 126, 254, 510, 1022, 2046, 4094, 8190, 16382, 32766, 65534, 131070, 262142, 524286, 1048574, 2097150, 4194302, 8388606, 16777214, 33554430, 67108862, 134217726, 268435454, 536870910, 1073741822, 2147483646, 4294967294, 8589934590, 17179869182, 34359738366, 68719476734, 137438953470, 274877906942, 549755813886, 1099511627774, 2199023255550, 4398046511102, 8796093022206, 17592186044414, 35184372088830, 70368744177662, 140737488355326, 281474976710654, 562949953421310, 1125899906842622, 2251799813685246, more...

integer, strictly-monotonic, +, A228038 (weak, multiple)

a(n)=∑[2*a(n-1)]
a(0)=2
∑(a)=partial sums of a
n≥0
4 operations
Recursive
a(n)=xor(2, 2*a(n-1))
a(0)=2
xor(a,b)=bitwise exclusive or
n≥0
5 operations
Recursive
a(n)=or(2, 2*a(n-1))
a(0)=2
or(a,b)=bitwise or
n≥0
5 operations
Recursive
a(n)=lcm(1+a(n-1), 2)
a(0)=2
lcm(a,b)=least common multiple
n≥0
5 operations
Recursive
a(n)=2^(2+n)-2
n≥0
7 operations
Power

Sequence ld5df4ga1pjwj

2, 6, 14, 30, 62, 127, 255, 511, 1023, 2047, 4095, 8191, 16383, 32767, 65535, more...

integer, strictly-monotonic, +, A228038 (weak, multiple)

a(n)=or(a(n-1), composite(a(n-1)))
a(0)=2
composite(n)=nth composite number
or(a,b)=bitwise or
n≥0
4 operations
Prime

Sequence somr5kz3q3n2j

2, 6, 15, 28, 55, 78, 119, 152, 207, 290, 341, 444, 533, 602, 705, 848, 1003, 1098, 1273, 1420, 1533, 1738, 1909, 2136, 2425, 2626, 2781, 2996, 3161, 3390, 3937, 4192, 4521, 4726, 5215, 5436, 5809, 6194, 6513, 6920, 7339, 7602, 8213, 8492, 8865, 9154, 9917, 10704, 11123, 11450, more...

integer, strictly-monotonic, +, A033286 (multiple)

a(n)=n*p(n)
p(n)=nth prime
n≥1
4 operations
Prime

Sequence nwo4dhdeeidmb

3, 6, 12, 48, 768, 196608, more...

integer, strictly-monotonic, +, A085866 (multiple)

a(n)=a(n-1)*φ(a(n-1))
a(0)=3
ϕ(n)=number of relative primes (Euler's totient)
n≥0
4 operations
Prime

Sequence 4xfpw53yryd3o

4, 3, 2, 4, 3, 2, 4, 3, 2, 4, 3, 2, 4, 3, 2, 4, 3, 2, 4, 3, 2, 4, 3, 2, 4, 3, 2, 4, 3, 2, 4, 3, 2, 4, 3, 2, 4, 3, 2, 4, 3, 2, 4, 3, 2, 4, 3, 2, 4, 3, more...

integer, periodic-3, non-monotonic, +, A244951 (weak, multiple)

a(n)=de[16/37]
de(a)=decimal expansion of a
n≥0
4 operations
Arithmetic

Sequence 5vdaomhza0vvh

5, 5, 10, 15, 20, 25, 30, 35, 56, 63, 70, 77, 132, 143, 182, 195, 208, 221, 306, 323, 380, 399, 418, 437, 552, 575, 598, 621, 644, 667, 870, 899, 992, 1023, 1054, 1085, 1116, 1147, 1406, 1443, 1480, 1517, 1722, 1763, 1892, 1935, 1978, 2021, 2256, 2303, more...

integer, monotonic, +, A242895 (weak, multiple)

a(n)=n*gpf(a(n-1))
a(0)=5
gpf(n)=greatest prime factor of n
n≥0
4 operations
Prime

Sequence su3nrhdtsc2b

5, 7, 13, 37, 151, 863, 6689, 67139, 843377, more...

integer, strictly-monotonic, +, A064600 (multiple)

a(n)=p(a(n-1)-1)
a(0)=5
p(n)=nth prime
n≥0
4 operations
Prime

Sequence soxv5xx3je1nm

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 2, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -4, 2, 0, 0, 2, -4, 2, 2, -4, 11, 311, -640, 311, 11, -4, 2, 0, 0, 923, 3158, -4081, more...

integer, non-monotonic, +-, A172546 (weak, multiple)

a(n)=Δ[Δ[pt(pt(n))]]
pt(n)=Pascals triangle by rows
Δ(a)=differences of a
n≥0
5 operations
Combinatoric

Sequence wybkbjnzvk0n

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

integer, non-monotonic, +-, A172546 (weak, multiple)

a(n)=Δ[agc(agc(∑[n]))]
∑(a)=partial sums of a
agc(n)=number of factorizations into prime powers (abelian group count)
Δ(a)=differences of a
n≥0
5 operations
Prime

Sequence s2ar4421mjlu

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

integer, non-monotonic, +-, A172546 (weak, multiple)

a(n)=Δ[agc(stern(φ(n)))]
ϕ(n)=number of relative primes (Euler's totient)
stern(n)=Stern-Brocot sequence
agc(n)=number of factorizations into prime powers (abelian group count)
Δ(a)=differences of a
n≥1
5 operations
Prime

Sequence 1cklvjwq4vj4j

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

integer, non-monotonic, +-, A172546 (weak, multiple)

a(n)=Δ[stern(stern(φ(n)))]
ϕ(n)=number of relative primes (Euler's totient)
stern(n)=Stern-Brocot sequence
Δ(a)=differences of a
n≥1
5 operations
Prime

Sequence o0bq3vc0sfxcc

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

integer, non-monotonic, +-, A172546 (weak, multiple)

a(n)=Δ[agc(composite(n)²)]
composite(n)=nth composite number
agc(n)=number of factorizations into prime powers (abelian group count)
Δ(a)=differences of a
n≥1
5 operations
Prime

Sequence ft2vzm203bn5f

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 1, -1, 0, 1, 2, -3, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 0, 0, 1, 0, -1, 0, 1, -1, 3, -2, -1, 3, 2, -5, 3, -2, -1, more...

integer, non-monotonic, +-, A172546 (weak, multiple)

a(n)=Δ[φ(stern(φ(n)))]
ϕ(n)=number of relative primes (Euler's totient)
stern(n)=Stern-Brocot sequence
Δ(a)=differences of a
n≥1
5 operations
Prime

Sequence yyuxzqiph0rqf

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

integer, non-monotonic, +-, A172546 (weak, multiple)

a(n)=Δ[log2(ω(τ(n)))]
τ(n)=number of divisors of n
ω(n)=number of distinct prime divisors of n
Δ(a)=differences of a
n≥2
5 operations
Prime
a(n)=Δ[p(ω(τ(n)))]
τ(n)=number of divisors of n
ω(n)=number of distinct prime divisors of n
p(n)=nth prime
Δ(a)=differences of a
n≥2
5 operations
Prime
a(n)=Δ[τ(ω(τ(n)))]
τ(n)=number of divisors of n
ω(n)=number of distinct prime divisors of n
Δ(a)=differences of a
n≥2
5 operations
Prime
a(n)=Δ[Ω(ω(τ(n)))]
τ(n)=number of divisors of n
ω(n)=number of distinct prime divisors of n
Ω(n)=number of prime divisors of n
Δ(a)=differences of a
n≥2
5 operations
Prime
a(n)=Δ[ω(ω(τ(n)))]
τ(n)=number of divisors of n
ω(n)=number of distinct prime divisors of n
Δ(a)=differences of a
n≥2
5 operations
Prime

Sequence fjjezokmsjsol

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 9, -9, 2, -2, 0, 0, 0, 0, 0, 0, 0, more...

integer, non-monotonic, +-, A172546 (weak, multiple)

a(n)=Δ[pt(pt(lpf(n)))]
lpf(n)=least prime factor of n
pt(n)=Pascals triangle by rows
Δ(a)=differences of a
n≥1
5 operations
Prime

Sequence go3w0u3i3mtqe

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 2, -2, 0, 2, -2, 9, -9, 9, -9, 2, -2, 0, 0, 0, 0, 0, 0, 923, more...

integer, non-monotonic, +-, A172546 (weak, multiple)

a(n)=Δ[pt(pt(rad(n)))]
rad(n)=square free kernel of n
pt(n)=Pascals triangle by rows
Δ(a)=differences of a
n≥1
5 operations
Prime

Sequence llf1mftgd2zhf

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 1, -1, 0, 2, -2, 0, 0, 1, -1, 0, 0, 2, -2, 1, -1, 9, -9, 2, -1, -1, 0, 0, 0, 0, 0, 0, more...

integer, non-monotonic, +-, A172546 (weak, multiple)

a(n)=Δ[pt(pt(gpf(n)))]
gpf(n)=greatest prime factor of n
pt(n)=Pascals triangle by rows
Δ(a)=differences of a
n≥1
5 operations
Prime

Sequence 2jvq32jrdifaf

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

integer, non-monotonic, +-, A172546 (weak, multiple)

a(n)=Δ[pt(φ(stern(n)))]
stern(n)=Stern-Brocot sequence
ϕ(n)=number of relative primes (Euler's totient)
pt(n)=Pascals triangle by rows
Δ(a)=differences of a
n≥1
5 operations
Prime

Sequence efmwdwa0oehhg

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

integer, non-monotonic, +-, A172546 (weak, multiple)

a(n)=Δ[agc(ceil(Λ(n)))]
Λ(n)=Von Mangoldt's function
agc(n)=number of factorizations into prime powers (abelian group count)
Δ(a)=differences of a
n≥1
5 operations
Prime

Sequence 0q4zecbtgt3x

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

integer, non-monotonic, +-, A172546 (weak, multiple)

a(n)=Δ[P(floor(Λ(n)))]
Λ(n)=Von Mangoldt's function
P(n)=partition numbers
Δ(a)=differences of a
n≥1
5 operations
Prime

Sequence ftbje42tucatm

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

integer, non-monotonic, +-, A172546 (weak, multiple)

a(n)=Δ[catalan(floor(Λ(n)))]
Λ(n)=Von Mangoldt's function
catalan(n)=the catalan numbers
Δ(a)=differences of a
n≥1
5 operations
Prime

Sequence gzqts30et2fhn

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 1, -1, 0, 0, 1, -1, 1, -1, 0, 0, 5, -5, 0, 0, 0, 0, 5, -5, 5, -5, 0, 0, 0, 0, 5, -5, 0, 0, 5, -5, 5, -5, 0, 0, 5, -5, 0, 0, 0, more...

integer, non-monotonic, +-, A172546 (weak, multiple)

a(n)=Δ[floor(Λ(n))!]
Λ(n)=Von Mangoldt's function
Δ(a)=differences of a
n≥1
5 operations
Prime

Sequence yerd3pfiqgmyl

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

integer, non-monotonic, +-, A172546 (weak, multiple)

a(n)=Δ[φ(stern(stern(n)))]
stern(n)=Stern-Brocot sequence
ϕ(n)=number of relative primes (Euler's totient)
Δ(a)=differences of a
n≥1
5 operations
Prime

Sequence tyqzzqxbojlzn

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

integer, non-monotonic, +-, A172546 (weak, multiple)

a(n)=Δ[φ(φ(stern(n)))]
stern(n)=Stern-Brocot sequence
ϕ(n)=number of relative primes (Euler's totient)
Δ(a)=differences of a
n≥1
5 operations
Prime

Sequence zk20rmh1aahlh

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 1, -1, 1, 0, 1, -2, 0, 1, 0, 0, -1, 1, 1, -1, -1, 1, 4, -4, 1, 0, 0, 0, 0, -1, 4, -5, 2, 0, 2, -3, 4, -3, 0, -2, 5, -3, 3, -3, 2, more...

integer, non-monotonic, +-, A172546 (weak, multiple)

a(n)=Δ[pt(φ(φ(n)))]
ϕ(n)=number of relative primes (Euler's totient)
pt(n)=Pascals triangle by rows
Δ(a)=differences of a
n≥1
5 operations
Prime

Sequence yalavw4u4sijm

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 1, -1, 1, 0, 2, -3, 1, 0, 0, 0, 2, -2, 2, -2, 0, 0, 2, -2, 2, 0, 0, 0, 0, -2, 2, -2, 2, 0, 4, -6, 2, 0, 0, 0, 6, -6, 0, 0, 4, more...

integer, non-monotonic, +-, A172546 (weak, multiple)

a(n)=Δ[φ(φ(φ(n)))]
ϕ(n)=number of relative primes (Euler's totient)
Δ(a)=differences of a
n≥1
5 operations
Prime

Sequence rzuq2lczhzvjn

0, 0, 0, 0, 0, 0, 0, 1, -2, 1, 0, 0, 0, 1, -2, 1, 1, 0, -3, 4, -4, 4, -4, 4, -4, 4, -4, 4, -3, 0, 1, 0, 0, 0, 1, 1, -3, -1, 2, 3, -4, 2, -4, 8, -8, 1, 2, 0, 2, more...

integer, non-monotonic, +-, A172564 (weak, multiple)

a(n)=Δ[Δ[pt(stern(n))]]
stern(n)=Stern-Brocot sequence
pt(n)=Pascals triangle by rows
Δ(a)=differences of a
n≥0
5 operations
Combinatoric

Sequence wgnn4zw5mnpgb

0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 9, -9, 0, 0, 0, 0, 0, 0, 0, 329, -329, 0, 405, -405, 0, 923, -923, 923, -923, 0, 0, 0, 0, 0, 121399651099, -121399651099, 538257874439, -538257874439, 405, 518, 158753388976, -158753389899, 0, 405, more...

integer, non-monotonic, +-, A172564 (weak, multiple)

a(n)=Δ[pt(pt(σ(n)))]
σ(n)=divisor sum of n
pt(n)=Pascals triangle by rows
Δ(a)=differences of a
n≥1
5 operations
Prime

Sequence 4um5xmpt0jtbp

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

integer, non-monotonic, +-, A172564 (weak, multiple)

a(n)=Δ[agc(lcm(n, 6))]
lcm(a,b)=least common multiple
agc(n)=number of factorizations into prime powers (abelian group count)
Δ(a)=differences of a
n≥0
5 operations
Prime

Sequence 1muijv034hrhj

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

integer, non-monotonic, +-, A172564 (weak, multiple)

a(n)=Δ[gcd(n, agc(n))]
agc(n)=number of factorizations into prime powers (abelian group count)
gcd(a,b)=greatest common divisor
Δ(a)=differences of a
n≥0
5 operations
Prime

Sequence a2ora3u42ussg

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

integer, non-monotonic, +-, A172564 (weak, multiple)

a(n)=Δ[agc(τ(stern(n)))]
stern(n)=Stern-Brocot sequence
τ(n)=number of divisors of n
agc(n)=number of factorizations into prime powers (abelian group count)
Δ(a)=differences of a
n≥1
5 operations
Prime

Sequence xq51ji3505ywl

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

integer, non-monotonic, +-, A172564 (weak, multiple)

a(n)=Δ[stern(τ(stern(n)))]
stern(n)=Stern-Brocot sequence
τ(n)=number of divisors of n
Δ(a)=differences of a
n≥1
5 operations
Prime

Sequence bhjnjzekucsqi

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

integer, non-monotonic, +-, A172564 (weak, multiple)

a(n)=Δ[agc(composite(stern(n)))]
stern(n)=Stern-Brocot sequence
composite(n)=nth composite number
agc(n)=number of factorizations into prime powers (abelian group count)
Δ(a)=differences of a
n≥1
5 operations
Prime

Sequence bego51tdmizao

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

integer, non-monotonic, +-, A172564 (weak, multiple)

a(n)=Δ[φ(τ(stern(n)))]
stern(n)=Stern-Brocot sequence
τ(n)=number of divisors of n
ϕ(n)=number of relative primes (Euler's totient)
Δ(a)=differences of a
n≥1
5 operations
Prime

Sequence 04wivh5cpoupj

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

integer, non-monotonic, +-, A172564 (weak, multiple)

a(n)=Δ[P(Ω(stern(n)))]
stern(n)=Stern-Brocot sequence
Ω(n)=number of prime divisors of n
P(n)=partition numbers
Δ(a)=differences of a
n≥1
5 operations
Prime

Sequence 1mkedje0nmpwb

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

integer, non-monotonic, +-, A172564 (weak, multiple)

a(n)=Δ[catalan(Ω(stern(n)))]
stern(n)=Stern-Brocot sequence
Ω(n)=number of prime divisors of n
catalan(n)=the catalan numbers
Δ(a)=differences of a
n≥1
5 operations
Prime

Sequence o0our00rzrlvh

0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 1, -1, 0, 1, -1, 0, 5, -5, 0, 0, 0, 0, 5, -5, 0, 1, -1, 0, 1, -1, 1, 0, -1, 0, 1, -1, 0, 5, -5, 0, 5, -5, 1, -1, 1, -1, 5, more...

integer, non-monotonic, +-, A172564 (weak, multiple)

a(n)=Δ[Ω(stern(n))!]
stern(n)=Stern-Brocot sequence
Ω(n)=number of prime divisors of n
Δ(a)=differences of a
n≥1
5 operations
Prime

Sequence 2m31s2b1fwzmf

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

integer, non-monotonic, +-, A172565 (weak, multiple)

a(n)=Δ[τ(agc(agc(n)))]
agc(n)=number of factorizations into prime powers (abelian group count)
τ(n)=number of divisors of n
Δ(a)=differences of a
n≥0
5 operations
Prime
a(n)=Δ[Ω(agc(agc(n)))]
agc(n)=number of factorizations into prime powers (abelian group count)
Ω(n)=number of prime divisors of n
Δ(a)=differences of a
n≥0
5 operations
Prime
a(n)=Δ[ω(agc(agc(n)))]
agc(n)=number of factorizations into prime powers (abelian group count)
ω(n)=number of distinct prime divisors of n
Δ(a)=differences of a
n≥0
5 operations
Prime

Sequence ygjh45hbodq1f

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

integer, non-monotonic, +-, A172565 (weak, multiple)

a(n)=Δ[pt(σ(agc(n)))]
agc(n)=number of factorizations into prime powers (abelian group count)
σ(n)=divisor sum of n
pt(n)=Pascals triangle by rows
Δ(a)=differences of a
n≥0
5 operations
Prime

Sequence x1unpt5z4eqfc

0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 1, -1, 0, 0, 0, 3, -3, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, more...

integer, non-monotonic, +-, A172565 (weak, multiple)

a(n)=Δ[p(agc(agc(n)))]
agc(n)=number of factorizations into prime powers (abelian group count)
p(n)=nth prime
Δ(a)=differences of a
n≥0
5 operations
Prime

Sequence cqm5l2q13aj4e

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

integer, non-monotonic, +-, A172565 (weak, multiple)

a(n)=Δ[catalan(agc(agc(n)))]
agc(n)=number of factorizations into prime powers (abelian group count)
catalan(n)=the catalan numbers
Δ(a)=differences of a
n≥0
5 operations
Prime

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