Sequence Database

A database with 2076264 machine generated integer and decimal sequences.

Displaying result 0-99 of total 140956. [0] [1] [2] [3] [4] ... [1409]

Sequence fvggmj41sayzg

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

integer, monotonic, +, A080405 (weak, multiple)

a(n)=ω(catalan(n))
catalan(n)=the catalan numbers
ω(n)=number of distinct prime divisors of n
n≥0
3 operations
Prime

Sequence pay3g3ioqircn

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

integer, non-monotonic, +, A081399 (weak)

a(n)=Ω(catalan(n))
catalan(n)=the catalan numbers
Ω(n)=number of prime divisors of n
n≥0
3 operations
Prime
a(n)=ceil(log2(τ(catalan(n))))
catalan(n)=the catalan numbers
τ(n)=number of divisors of n
n≥0
5 operations
Prime

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 EulerGamma=0.5772... (Euler Gamma)
contfrac(a)=continued fraction of a
n≥0
3 operations
Power

Sequence txkmuesaztw4g

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, -1, 0, 0, -1, 1, 0, -1, 0, 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 it0jhqdeappbm

1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, 1, -1, -1, -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
a(n)=(-1)^Ω(P(n))
P(n)=partition numbers
Ω(n)=number of prime divisors of n
n≥0
6 operations
Prime
a(n)=μ(or(6, Ω(P(n))))
P(n)=partition numbers
Ω(n)=number of prime divisors of n
or(a,b)=bitwise or
μ(n)=Möbius function
n≥0
6 operations
Prime

Sequence varyrbggkaicp

1, 1, 1, 4, 6, 12, 40, 240, 480, 1920, 6912, 20736, more...

integer, monotonic, +, A062624 (weak)

a(n)=φ(catalan(n))
catalan(n)=the catalan numbers
ϕ(n)=number of relative primes (Euler's totient)
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 gosi1r5nlnpnf

1, 1, 2, 2, 4, 8, 12, 8, 16, 16, 24, 32, more...

integer, non-monotonic, +, A152763 (weak)

a(n)=τ(catalan(n))
catalan(n)=the catalan numbers
τ(n)=number of divisors of n
n≥0
3 operations
Prime

Sequence t3txw0hqmwthe

1, 1, 2, 4, 8, 16, 30, 60, 96, more...

integer, monotonic, +, A027423 (weak)

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

Sequence yref1ithc1qhj

1, 1, 2, 5, 14, 42, 66, 429, 1430, 4862, 8398, 58786, more...

integer, monotonic, +, A281594 (weak)

a(n)=rad(catalan(n))
catalan(n)=the catalan numbers
rad(n)=square free kernel of n
n≥0
3 operations
Prime

Sequence gaaiynoaqgfob

1, 1, 2, 6, 20, 96, 582, 4672, 47330, 595680, more...

integer, monotonic, +, A131842 (weak)

a(n)=Δ[p(a(n-1))]
a(0)=1
p(n)=nth prime
Δ(a)=differences of a
n≥0
3 operations
Prime
a(n)=Δ[or(p(a(n-1)), ω(n))]
a(0)=1
p(n)=nth prime
ω(n)=number of distinct prime divisors of n
or(a,b)=bitwise or
Δ(a)=differences of a
n≥0
6 operations
Prime
a(n)=Δ[exp(abs(log(p(a(n-1)))))]
a(0)=1
p(n)=nth prime
Δ(a)=differences of a
n≥0
6 operations
Prime
a(n)=Δ[sqrt(floor(p(a(n-1))²))]
a(0)=1
p(n)=nth prime
Δ(a)=differences of a
n≥0
6 operations
Prime
a(n)=Δ[-floor(-p(gpf(a(n-1))))]
a(0)=1
gpf(n)=greatest prime factor of n
p(n)=nth prime
Δ(a)=differences of a
n≥0
7 operations
Prime

Sequence u1woduobho3jo

1, 1, 2, 7, 135, 53174, 6620830889, more...

integer, monotonic, +, A120379 (weak)

a(n)=P(catalan(n))
catalan(n)=the catalan numbers
P(n)=partition numbers
n≥0
3 operations
Combinatoric

Sequence j4i5dglg43wdc

1, 1, 2, 10, 140, 5880, 776160, 332972640, 476150875200, 2315045555222400, more...

integer, monotonic, +, A003046 (weak, multiple)

a(n)=∏[catalan(n)]
catalan(n)=the catalan numbers
∏(a)=partial products of a
n≥0
3 operations
Combinatoric
a(n)=∏[sqrt(floor(catalan(n)²))]
catalan(n)=the catalan numbers
∏(a)=partial products of a
n≥0
6 operations
Combinatoric
a(n)=∏[exp(abs(log(catalan(n))))]
catalan(n)=the catalan numbers
∏(a)=partial products of a
n≥0
6 operations
Combinatoric
a(n)=∏[xor(1, xor(1, catalan(n)))]
catalan(n)=the catalan numbers
xor(a,b)=bitwise exclusive or
∏(a)=partial products of a
n≥0
7 operations
Combinatoric
a(n)=∏[and(Δ[-n], catalan(n))]
Δ(a)=differences of a
catalan(n)=the catalan numbers
and(a,b)=bitwise and
∏(a)=partial products of a
n≥0
7 operations
Combinatoric

Sequence y5ybwgud1kkde

1, 1, 3, 1, 1, 3, 1, 1, 9, 1, 1, 3, 1, 1, 3, 1, 1, 9, 1, 1, 3, 1, 1, 3, 1, 1, 9, 1, 1, 3, 1, 1, 3, 1, 1, 9, 1, 1, 3, 1, 1, 3, 1, 1, 9, 1, 1, 3, 1, 1, more...

integer, periodic-9, non-monotonic, +, A139378 (weak, multiple)

a(n)=gcd(n, 9)
gcd(a,b)=greatest common divisor
n≥1
3 operations
Divisibility

Sequence jo0xalmuopsfg

1, 1, 3, 6, 24, 96, 336, 672, 3024, 9072, 35280, 120960, more...

integer, monotonic, +, A152761 (weak)

a(n)=σ(catalan(n))
catalan(n)=the catalan numbers
σ(n)=divisor sum of n
n≥0
3 operations
Prime

Sequence zewbm3rryknyn

1, 1, 3, 12, 60, 360, 2418, 19344, 159120, more...

integer, monotonic, +, A062569 (weak)

a(n)=σ(n!)
σ(n)=divisor sum of n
n≥0
3 operations
Prime

Sequence yquxgtzi25ljk

1, 2, 5, 7, 7, 11, 13, 13, 17, 19, 19, more...

integer, monotonic, +, A093413 (weak, multiple)

a(n)=gpf(catalan(n))
catalan(n)=the catalan numbers
gpf(n)=greatest prime factor of n
n≥1
3 operations
Prime

Sequence u2m3kx21yh4fi

1, 9, 36, 84, 126, 126, 84, 36, 9, 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, 0, more...

integer, non-monotonic, +, A285198 (weak, multiple)

a(n)=C(9, n)
C(n,k)=binomial coefficient
n≥0
3 operations
Combinatoric
a(n)=(10/n-1)*a(n-1)
a(0)=1
n≥0
7 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
a(n)=(11/n-1)*a(n-1)
a(0)=1
n≥0
7 operations
Recursive

Sequence bblnuylbxwbep

1, 11, 55, 165, 330, 462, 462, 330, 165, 55, 11, 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, more...

integer, non-monotonic, +, A010927 (weak, multiple)

a(n)=C(11, n)
C(n,k)=binomial coefficient
n≥0
3 operations
Combinatoric
a(n)=(12/n-1)*a(n-1)
a(0)=1
n≥0
7 operations
Recursive

Sequence udc2frmnd4rbg

2, 2, 3, 13, 89, 659, 5443, 49033, 484037, more...

integer, monotonic, +, A062439 (weak)

a(n)=p(n!)
p(n)=nth prime
n≥0
3 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 xhwip5ylxgoxm

2, 5, 2, 2, 2, 3, 2, 2, 2, 2, more...

integer, non-monotonic, +, A152765 (weak, multiple)

a(n)=lpf(catalan(n))
catalan(n)=the catalan numbers
lpf(n)=least prime factor of n
n≥2
3 operations
Prime

Sequence hkgycojerewfb

0, -1, -1, -2, 0, -5, 19, 354, 125308, 15702094855, more...

integer, non-monotonic, +-, A153059 (weak)

a(n)=a(n-1)²-n
a(0)=0
n≥0
4 operations
Recursive
a(n)=(a(n-1)*λ(n))²-n
a(0)=0
λ(n)=Liouville's function
n≥0
7 operations
Prime
a(n)=a(n-1)²-gcd(n, n!)
a(0)=0
gcd(a,b)=greatest common divisor
n≥0
7 operations
Combinatoric
a(n)=a(n-1)²-lcm(n, lpf(n))
a(0)=0
lpf(n)=least prime factor of n
lcm(a,b)=least common multiple
n≥0
7 operations
Prime
a(n)=a(n-1)²-Ω(2^n)
a(0)=0
Ω(n)=number of prime divisors of n
n≥0
7 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[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
4 operations
Prime
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[catalan(ω(τ(n)))]
τ(n)=number of divisors of n
ω(n)=number of distinct prime divisors of n
catalan(n)=the catalan numbers
Δ(a)=differences of a
n≥2
5 operations
Prime
a(n)=Δ[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)=partition numbers
Δ(a)=differences of a
n≥2
5 operations
Prime

Sequence vpqtlss0tlhid

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, 320, -320, -9, 2, -2, 0, 0, 0, 923, 4081, 0, -4081, more...

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

a(n)=Δ[pt(pt(n))]
pt(n)=Pascals triangle by rows
Δ(a)=differences of a
n≥1
4 operations
Combinatoric

Sequence cdzpmpxuwly1h

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

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

a(n)=Δ[pt(stern(n))]
stern(n)=Stern-Brocot sequence
pt(n)=Pascals triangle by rows
Δ(a)=differences of a
n≥1
4 operations
Combinatoric
a(n)=Δ[and(7, pt(stern(n)))]
stern(n)=Stern-Brocot sequence
pt(n)=Pascals triangle by rows
and(a,b)=bitwise and
Δ(a)=differences of a
n≥1
6 operations
Combinatoric
a(n)=Δ[xor(8, pt(stern(n)))]
stern(n)=Stern-Brocot sequence
pt(n)=Pascals triangle by rows
xor(a,b)=bitwise exclusive or
Δ(a)=differences of a
n≥1
6 operations
Combinatoric
a(n)=Δ[or(8, pt(stern(n)))]
stern(n)=Stern-Brocot sequence
pt(n)=Pascals triangle by rows
or(a,b)=bitwise or
Δ(a)=differences of a
n≥1
6 operations
Combinatoric

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
a(n)=Δ[1+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
6 operations
Prime
a(n)=Δ[and(7, φ(agc(n)))]
agc(n)=number of factorizations into prime powers (abelian group count)
ϕ(n)=number of relative primes (Euler's totient)
and(a,b)=bitwise and
Δ(a)=differences of a
n≥0
6 operations
Prime
a(n)=Δ[xor(8, φ(agc(n)))]
agc(n)=number of factorizations into prime powers (abelian group count)
ϕ(n)=number of relative primes (Euler's totient)
xor(a,b)=bitwise exclusive or
Δ(a)=differences of a
n≥0
6 operations
Prime
a(n)=Δ[or(8, φ(agc(n)))]
agc(n)=number of factorizations into prime powers (abelian group count)
ϕ(n)=number of relative primes (Euler's totient)
or(a,b)=bitwise or
Δ(a)=differences of a
n≥0
6 operations
Prime

Sequence tmkzmkedac2vl

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

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

a(n)=Δ[pt(stern(n))]
stern(n)=Stern-Brocot sequence
pt(n)=Pascals triangle by rows
Δ(a)=differences of a
n≥2
4 operations
Combinatoric
a(n)=Δ[and(7, pt(stern(n)))]
stern(n)=Stern-Brocot sequence
pt(n)=Pascals triangle by rows
and(a,b)=bitwise and
Δ(a)=differences of a
n≥2
6 operations
Combinatoric
a(n)=Δ[xor(8, pt(stern(n)))]
stern(n)=Stern-Brocot sequence
pt(n)=Pascals triangle by rows
xor(a,b)=bitwise exclusive or
Δ(a)=differences of a
n≥2
6 operations
Combinatoric
a(n)=Δ[or(8, pt(stern(n)))]
stern(n)=Stern-Brocot sequence
pt(n)=Pascals triangle by rows
or(a,b)=bitwise or
Δ(a)=differences of a
n≥2
6 operations
Combinatoric

Sequence apkwicb1gqkrj

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, 0, more...

integer, non-monotonic, +-, A172577 (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≥1
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≥1
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≥1
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≥1
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≥1
5 operations
Prime

Sequence hyne1ahjkr42f

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, 0, more...

integer, non-monotonic, +-, A172577 (weak, multiple)

a(n)=Δ[agc(n²)]
agc(n)=number of factorizations into prime powers (abelian group count)
Δ(a)=differences of a
n≥1
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≥1
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≥1
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≥1
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≥1
5 operations
Prime

Sequence wwjg42mttrtff

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, 0, more...

integer, non-monotonic, +-, A172577 (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≥1
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≥1
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≥1
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≥1
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≥1
5 operations
Prime

Sequence 2si1m0qry0k1g

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, 0, more...

integer, non-monotonic, +-, A172577 (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≥1
4 operations
Prime
a(n)=Δ[1+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≥1
6 operations
Prime
a(n)=Δ[and(7, φ(agc(n)))]
agc(n)=number of factorizations into prime powers (abelian group count)
ϕ(n)=number of relative primes (Euler's totient)
and(a,b)=bitwise and
Δ(a)=differences of a
n≥1
6 operations
Prime
a(n)=Δ[xor(8, φ(agc(n)))]
agc(n)=number of factorizations into prime powers (abelian group count)
ϕ(n)=number of relative primes (Euler's totient)
xor(a,b)=bitwise exclusive or
Δ(a)=differences of a
n≥1
6 operations
Prime
a(n)=Δ[or(8, φ(agc(n)))]
agc(n)=number of factorizations into prime powers (abelian group count)
ϕ(n)=number of relative primes (Euler's totient)
or(a,b)=bitwise or
Δ(a)=differences of a
n≥1
6 operations
Prime

Sequence uri31xx2pnfmp

0, 0, 0, 0, 42, more...

integer, monotonic, +, A167654 (weak)

a(n)=C(catalan(n), 41)
catalan(n)=the catalan numbers
C(n,k)=binomial coefficient
n≥1
4 operations
Combinatoric

Sequence mniclyfidn4ym

0, 0, 0, 5, 1001, 111930, 12082785, 1391641251, 173503885555, 23254794293445, 3314798008593435, more...

integer, monotonic, +, A119549 (weak)

a(n)=C(catalan(n), 4)
catalan(n)=the catalan numbers
C(n,k)=binomial coefficient
n≥0
4 operations
Combinatoric

Sequence kzvuytsopq4lo

0, 0, 0, 10, 364, 11480, 374660, 13067054, 486345860, 19143687420, 789566607180, 33856987804640, 1500056631216220, more...

integer, monotonic, +, A051790 (weak)

a(n)=C(catalan(n), 3)
catalan(n)=the catalan numbers
C(n,k)=binomial coefficient
n≥0
4 operations
Combinatoric

Sequence gxz1kqg0p03ah

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

integer, monotonic, +, A080405 (weak, multiple)

a(n)=Ω(τ(catalan(n)))
catalan(n)=the catalan numbers
τ(n)=number of divisors of n
Ω(n)=number of prime divisors of n
n≥0
4 operations
Prime
a(n)=floor(log2(τ(catalan(n))))
catalan(n)=the catalan numbers
τ(n)=number of divisors of n
n≥0
5 operations
Prime

Sequence v5uzdbzivs0rk

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

integer, non-monotonic, +, A035454 (weak, multiple)

a(n)=ω(∑[catalan(n)])
catalan(n)=the catalan numbers
∑(a)=partial sums of a
ω(n)=number of distinct prime divisors of n
n≥0
4 operations
Prime

Sequence wcswpnkhelajj

0, 1, 2, 3, 7, 14, 17, 18, 19, 21, 146, 161, 162, 164, 172, 175, 178, 179, 180, 184, 185, 187, 188, 191, 192, 475, 492, 500, 501, 502, 550, 551, 553, 554, 555, 567, 568, 569, 575, 576, 582, 583, 586, 594, 595, 598, 606, 607, 616, 617, more...

integer, strictly-monotonic, +, A073827 (weak, multiple)

a(n)=∑[contfrac[sin(37)]]
contfrac(a)=continued fraction of a
∑(a)=partial sums of a
n≥0
4 operations
Trigonometric

Sequence tuzomv5hzgw2n

0, 1, 2, 4, 12, 1, 2, 12, 5, 1, 10, 2, 3, 8, 13, 1, 3, 9, 14, 10, 10, 1, 10, 1, 13, 1, 11, 5, 1, 1, 1, 8, 1, 1, 1, 1, 11, 4, 1, 2, 1, 5, 2, 1, 2, 1, 25, 45, 1, 1, more...

integer, non-monotonic, +, A215795 (weak, multiple)

a(n)=contfrac[sin(43)²]
contfrac(a)=continued fraction of a
n≥0
4 operations
Trigonometric

Sequence xs521w3bsisde

0, 1, 3, 1, 4, 1, 1, 1, 2, 39, 4, 2, 6, 1, 5, 29, 6, 1, 2, 1, 21, 1, 2, 1, 3, 2, 2, 4, 1, 21, 6, 1, 3, 4, 3, 1, 6, 1, 1, 1, 1, 4, 1, 1, 1, 39, 3, 1, 1, 2, more...

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

a(n)=contfrac[tan(sin(51))]
contfrac(a)=continued fraction of a
n≥0
4 operations
Trigonometric

Sequence p0bhjuhftgx1b

0, 1, 3, 1, 4, 1, 1, 2, 5, 1, 2, 9, 1, 1, 6, 1, 3, 3, 2, 4, 3, 2, 2, 1, 2, 1, 1, 7, 28, 1, 1, 5, 2, 1, 5, 1, 30, 1, 5, 3, 10, 1, 14, 15, 1, 2, 1, 5, 1, 1, more...

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

a(n)=contfrac[GlaisherKinkelin/ϕ]
GlaisherKinkelin=1.2824... (Glaisher-Kinkelin)
ϕ GoldenRatio=1.618... (Golden Ratio)
contfrac(a)=continued fraction of a
n≥0
4 operations
Arithmetic

Sequence ev4ym4hrgo1cg

0, 1, 3, 1, 4, 1, 1, 4, 2, 2, 2, 1, 20, 1, 28, 3, 2, 1, 4, 2, 11, 7, 1, 7, 2, 1, 1, 2, 1, 2, 3, 1, 1, 2, 1, 1, 1, 2, 1, 285, 1, 5, 1, 1, 20, 1, 2, 2, 4, 23, more...

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

a(n)=contfrac[tanh(tan(84))]
contfrac(a)=continued fraction of a
n≥0
4 operations
Trigonometric

Sequence ieexqlwxgmtub

0, 1, 3, 1, 4, 1, 1, 7, 37, 3, 1, 1, 35, 2, 5, 1, 4, 2, 1, 3, 23, 1, 3, 1, 5, 2, 4, 1, 25, 2, 1, 12, 4, 3, 3, 4, 1, 1, 37, 13, 16, 1, 2, 1, 2, 1, 1, 2, 23, 5, more...

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

a(n)=contfrac[acot(cos(63))]
contfrac(a)=continued fraction of a
n≥0
4 operations
Trigonometric

Sequence qmyg31xbhtzwl

0, 1, 3, 2, 5, 6, 7, more...

integer, non-monotonic, +, A153152 (weak)

a(n)=rad(n^a(n-1))
a(0)=0
rad(n)=square free kernel of n
n≥1
4 operations
Prime
a(n)=and(7, rad(n^floor(a(n-1))))
a(0)=0
rad(n)=square free kernel of n
and(a,b)=bitwise and
n≥1
7 operations
Prime
a(n)=ω(n)*gpf(n^a(n-1))
a(0)=0
ω(n)=number of distinct prime divisors of n
gpf(n)=greatest prime factor of n
n≥1
7 operations
Prime
a(n)=lcm(gpf(n^a(n-1)), Ω(n))
a(0)=0
gpf(n)=greatest prime factor of n
Ω(n)=number of prime divisors of n
lcm(a,b)=least common multiple
n≥1
7 operations
Prime
a(n)=n-λ(3^(a(n-1)+a(n-2)))
a(0)=0
a(1)=1
λ(n)=Liouville's function
n≥0
8 operations
Prime

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

Sequence 5e4dox0mgcfpo

0, 1, 4, 9, 16, 49, 64, 81, 100, 121, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625, 676, 729, 841, 900, 961, 1024, 1089, 1156, 1225, 1296, 1369, 1444, 1521, 1600, 1681, 1764, 1849, 1936, 2025, 2116, 2209, 2304, 2401, 2500, more...

integer, strictly-monotonic, +, A291216 (weak, multiple)

a(n)=comp[σ(a(n-1))]²
a(0)=5
σ(n)=divisor sum of n
comp(a)=complement function of a (in range)
n≥0
4 operations
Prime

Sequence 3cu3dbeu4gerc

0, 1, 5, 6, 2, 5, more...

integer, non-monotonic, +, A021068 (weak)

a(n)=de[1/64]
de(a)=decimal expansion of a
n≥0
4 operations
Arithmetic

Sequence osfdjlqjwxucg

1, -2, 10, -80, 880, -12320, 209440, -4188800, 96342400, -2504902400, 72642169600, -2324549427200, 81359229952000, -3091650738176000, more...

integer, non-monotonic, +-, A133480 (weak, multiple)

a(n)=∏[a(n-1)-3]
a(0)=1
∏(a)=partial products of a
n≥0
4 operations
Recursive
a(n)=∏[1-3*n]
∏(a)=partial products of a
n≥0
6 operations
Arithmetic
a(n)=∏[a(n-1)-or(3, ω(n))]
a(0)=1
ω(n)=number of distinct prime divisors of n
or(a,b)=bitwise or
∏(a)=partial products of a
n≥0
7 operations
Prime
a(n)=∏[a(n-1)-or(3, Ω(n))]
a(0)=1
Ω(n)=number of prime divisors of n
or(a,b)=bitwise or
∏(a)=partial products of a
n≥0
7 operations
Prime
a(n)=∏[a(n-1)-gcd(n!, 3)]
a(0)=1
gcd(a,b)=greatest common divisor
∏(a)=partial products of a
n≥2
7 operations
Combinatoric

Sequence a1aroshagizoe

1, 0, -1, 1, 2, 3, 7, 46, 2109, 4447835, 19783236185116, more...

integer, non-monotonic, +-, A058181 (weak)

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

Sequence robgd1iabqkih

1, 0, 1, 1, 2, 5, 27, 734, 538783, 290287121823, more...

integer, non-monotonic, +, A058182 (weak)

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

Sequence krm1o4fu23rpp

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

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

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

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
a(n)=-λ(p(n)*σ(φ(n)))
p(n)=nth prime
ϕ(n)=number of relative primes (Euler's totient)
σ(n)=divisor sum of n
λ(n)=Liouville's function
n≥1
8 operations
Prime

Sequence jog3swipzfpmi

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -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(sqrt(n)))
λ(n)=Liouville's function
n≥2
4 operations
Prime
a(n)=or(1, μ(floor(sqrt(n))))
μ(n)=Möbius function
or(a,b)=bitwise or
n≥2
6 operations
Prime
a(n)=λ(φ(n))^τ(n)*a(n-1)
a(0)=1
ϕ(n)=number of relative primes (Euler's totient)
λ(n)=Liouville's function
τ(n)=number of divisors of n
n≥2
8 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
a(n)=μ(catalan(floor(log2(n))))
catalan(n)=the catalan numbers
μ(n)=Möbius function
n≥2
5 operations
Prime
a(n)=or(1, μ(floor(log2(n))))
μ(n)=Möbius function
or(a,b)=bitwise or
n≥2
6 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 yzo10wilkbc0b

1, 1, -1, -1, -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, -1, -1, 0, -1, 1, -1, -1, -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 ntwp1gymd1icd

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, 1, -1, 1, -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
a(n)=or(1, μ(round(sqrt(n))))
μ(n)=Möbius function
or(a,b)=bitwise or
n≥1
6 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
a(n)=or(1, μ(Ω(∑[n])))
∑(a)=partial sums of a
Ω(n)=number of prime divisors of n
μ(n)=Möbius function
or(a,b)=bitwise or
n≥2
6 operations
Prime
a(n)=(-1)^Ω(Ω(∑[n]))
∑(a)=partial sums of a
Ω(n)=number of prime divisors of n
n≥2
7 operations
Prime
a(n)=-λ(p(n)*Ω(∑[n]))
p(n)=nth prime
∑(a)=partial sums of a
Ω(n)=number of prime divisors of n
λ(n)=Liouville's function
n≥2
8 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
a(n)=(-1)^Ω(or(1, n))
or(a,b)=bitwise or
Ω(n)=number of prime divisors of n
n≥0
7 operations
Prime
a(n)=or(1, λ(or(n, a(n-1)²)))
a(0)=1
or(a,b)=bitwise or
λ(n)=Liouville's function
n≥0
7 operations
Prime

Sequence 0u4lbk5is2drk

1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, -1, 1, -1, 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(23+n)
λ(n)=Liouville's function
n≥2
4 operations
Prime

Sequence kjmdohky4jvkn

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, 0, 0, 0, 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 1k5typwj1vhvh

1, 1, -1, -1, -1, -1, -1, 1, -1, -1, 1, -1, 1, -1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, 1, 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(37+n)
λ(n)=Liouville's function
n≥2
4 operations
Prime

Sequence qldj2a4xq4dzb

1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, 1, -1, -1, 1, -1, -1, -1, -1, -1, 1, -1, 1, -1, -1, 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 dltpjbm0pmldd

1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, -1, -1, 1, -1, -1, 1, -1, 1, 1, -1, -1, -1, 1, -1, -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(lcm(n, 94))
lcm(a,b)=least common multiple
λ(n)=Liouville's function
n≥1
4 operations
Prime

Sequence zihn2id1vk4db

1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, -1, -1, 1, -1, -1, 1, -1, 1, 1, -1, -1, -1, 1, -1, -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(lcm(n, 86))
lcm(a,b)=least common multiple
λ(n)=Liouville's function
n≥1
4 operations
Prime

Sequence yretg1wrgqv0i

1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, -1, -1, 1, -1, -1, 1, -1, 1, 1, -1, -1, -1, 1, -1, -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(lcm(n, 82))
lcm(a,b)=least common multiple
λ(n)=Liouville's function
n≥1
4 operations
Prime

Sequence h1tqzjl4uuqcd

1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, -1, -1, 1, -1, -1, 1, -1, 1, 1, -1, -1, -1, 1, -1, -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(lcm(n, 74))
lcm(a,b)=least common multiple
λ(n)=Liouville's function
n≥1
4 operations
Prime

Sequence 3h2ojrr5gqli

1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, -1, -1, 1, -1, -1, 1, -1, 1, 1, -1, -1, -1, 1, -1, -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(lcm(n, 62))
lcm(a,b)=least common multiple
λ(n)=Liouville's function
n≥1
4 operations
Prime

Sequence owhnv4zjsd2nd

1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, -1, -1, 1, -1, -1, 1, -1, 1, 1, -1, -1, -1, 1, -1, -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(lcm(n, 58))
lcm(a,b)=least common multiple
λ(n)=Liouville's function
n≥1
4 operations
Prime

Sequence fi5zkb3ktklkj

1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, -1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -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(lcm(n, 46))
lcm(a,b)=least common multiple
λ(n)=Liouville's function
n≥1
4 operations
Prime

Sequence wycukvp2gk5ab

1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, 1, -1, -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(lcm(n, 38))
lcm(a,b)=least common multiple
λ(n)=Liouville's function
n≥1
4 operations
Prime

Sequence znobwzsevpflo

1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, 1, -1, -1, -1, 1, -1, -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(lcm(n, 34))
lcm(a,b)=least common multiple
λ(n)=Liouville's function
n≥1
4 operations
Prime

Sequence luqgmihxz2cnn

1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, -1, -1, 1, 1, -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(lcm(n, 26))
lcm(a,b)=least common multiple
λ(n)=Liouville's function
n≥1
4 operations
Prime

Sequence 1qvqvoqljob5k

1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, -1, -1, -1, -1, 1, -1, -1, 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
a(n)=1/λ(rad(P(n)))
P(n)=partition numbers
rad(n)=square free kernel of n
λ(n)=Liouville's function
n≥0
6 operations
Prime
a(n)=or(1, λ(rad(P(n))))
P(n)=partition numbers
rad(n)=square free kernel of n
λ(n)=Liouville's function
or(a,b)=bitwise or
n≥0
6 operations
Prime

Sequence qrpvgo5gtojud

1, 1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, -1, -1, 1, -1, -1, 1, -1, 1, 1, 1, -1, -1, 1, -1, -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(lcm(n, 22))
lcm(a,b)=least common multiple
λ(n)=Liouville's function
n≥1
4 operations
Prime

Sequence 12sbyzb2uwgi

1, 1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, -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(24, n))
or(a,b)=bitwise or
λ(n)=Liouville's function
n≥1
4 operations
Prime

Sequence weylhshnpi1bl

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3628800, more...

integer, monotonic, +, A061603 (weak, multiple)

a(n)=C(n, 9)!
C(n,k)=binomial coefficient
n≥0
4 operations
Combinatoric
a(n)=n!^C(n, 10)
C(n,k)=binomial coefficient
n≥0
6 operations
Combinatoric
a(n)=C(P(pt(n)), 3)!
pt(n)=Pascals triangle by rows
P(n)=partition numbers
C(n,k)=binomial coefficient
n≥1
6 operations
Combinatoric
a(n)=C(n, composite(4+a(n-1)))!
a(0)=1
composite(n)=nth composite number
C(n,k)=binomial coefficient
n≥0
7 operations
Prime
a(n)=C(Δ[p(pt(n))], 3)!
pt(n)=Pascals triangle by rows
p(n)=nth prime
Δ(a)=differences of a
C(n,k)=binomial coefficient
n≥0
7 operations
Prime

Sequence sei3i1ir0gbfd

1, 1, 1, 1, 1, 1, 1, 1, 1, 3628800, more...

integer, monotonic, +, A068158 (weak, multiple)

a(n)=C(n, 9)!
C(n,k)=binomial coefficient
n≥1
4 operations
Combinatoric
a(n)=C(rad(n), 9)!
rad(n)=square free kernel of n
C(n,k)=binomial coefficient
n≥1
5 operations
Prime
a(n)=n!^C(n, 10)
C(n,k)=binomial coefficient
n≥1
6 operations
Combinatoric
a(n)=C(P(pt(n)), 3)!
pt(n)=Pascals triangle by rows
P(n)=partition numbers
C(n,k)=binomial coefficient
n≥2
6 operations
Combinatoric
a(n)=C(n, 7+Ω(n))!
Ω(n)=number of prime divisors of n
C(n,k)=binomial coefficient
n≥1
7 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 m2ncq5feihajo

1, 1, 1, 1, 2, 3, 3, 3, 5, 5, 5, more...

integer, monotonic, +, A216391 (weak)

a(n)=P(ω(catalan(n)))
catalan(n)=the catalan numbers
ω(n)=number of distinct prime divisors of n
P(n)=partition numbers
n≥0
4 operations
Prime
a(n)=gpf(∏[pt(τ(catalan(n)))])
catalan(n)=the catalan numbers
τ(n)=number of divisors of n
pt(n)=Pascals triangle by rows
∏(a)=partial products of a
gpf(n)=greatest prime factor of n
n≥0
6 operations
Prime

Sequence tbqomdqqmljae

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

integer, non-monotonic, +, A038082 (weak, multiple)

a(n)=agc(ceil(sqrt(n)))
agc(n)=number of factorizations into prime powers (abelian group count)
n≥2
4 operations
Prime

Sequence 44umi2nhwjbr

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

integer, non-monotonic, +, A038082 (weak, multiple)

a(n)=stern(ceil(sqrt(n)))
stern(n)=Stern-Brocot sequence
n≥2
4 operations
Recursive

Sequence lzyeezjgiigxb

1, 1, 1, 2, 4, 36, more...

integer, monotonic, +, A215251 (weak)

a(n)=stern(P(n)!)
P(n)=partition numbers
stern(n)=Stern-Brocot sequence
n≥0
4 operations
Combinatoric

Sequence laabt1341soeg

1, 1, 1, 3, 9, 40, more...

integer, monotonic, +, A020092 (weak)

a(n)=stern(∏[catalan(n)])
catalan(n)=the catalan numbers
∏(a)=partial products of a
stern(n)=Stern-Brocot sequence
n≥0
4 operations
Combinatoric

Sequence vnn2kqhtr3x2c

1, 1, 1, 3, 9, 72, 432, 21600, 1620000, 85860000, 9358740000, 4501553940000, more...

integer, monotonic, +, A305855 (weak, multiple)

a(n)=∏[stern(catalan(n))]
catalan(n)=the catalan numbers
stern(n)=Stern-Brocot sequence
∏(a)=partial products of a
n≥0
4 operations
Combinatoric
a(n)=stern(catalan(n))*a(n-1)
a(0)=1
catalan(n)=the catalan numbers
stern(n)=Stern-Brocot sequence
n≥0
5 operations
Combinatoric
a(n)=exp(∑[log(stern(catalan(n)))])
catalan(n)=the catalan numbers
stern(n)=Stern-Brocot sequence
∑(a)=partial sums of a
n≥0
6 operations
Combinatoric
a(n)=stern(rad(catalan(n)))*a(n-1)
a(0)=1
catalan(n)=the catalan numbers
rad(n)=square free kernel of n
stern(n)=Stern-Brocot sequence
n≥0
6 operations
Prime

Sequence ozk3y1tc5nawc

1, 1, 1, 4, 10, 1, 1, 15, 1, 1, 206, 1, 2, 121, 2, 4, 1, 23, 1, 4, 8, 3, 1, 1, 25, 16, 4, 4, 2, 4, 2, 1, 1, 3, 2, 6, 1, 18, 1, 6, 1, 5, 4, 2, 1, 3, 1, 6, 7, 1, more...

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

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

Sequence ehtt4kysr1htj

1, 1, 1, 4, 11, 3, 2, 1, 2, 1, 5, 2, 1, 2, 1, 1, 6, 2, 1, 3, 12, 6, 8, 4, 1, 11, 1, 2, 1, 1, 2, 1, 1, 4, 1, 5, 1, 7, 1, 20, 5, 4, 7, 1, 2, 3, 2, 1, 1, 4, more...

integer, non-monotonic, +, A048873 (weak, multiple)

a(n)=contfrac[root(9, 53)]
root(n,a)=the n-th root of a
contfrac(a)=continued fraction of a
n≥0
4 operations
Power

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 xudbtwraniqph

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

integer, non-monotonic, +, A237593 (weak)

a(n)=agc(stern(catalan(n)))
catalan(n)=the catalan numbers
stern(n)=Stern-Brocot sequence
agc(n)=number of factorizations into prime powers (abelian group count)
n≥1
4 operations
Prime

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 ij2g1ueg40uco

1, 1, 2, 3, 5, 11, 131, 39916931, more...

integer, monotonic, +, A075883 (weak)

a(n)=a(n-1)+a(n-2)!
a(0)=1
a(1)=1
n≥0
4 operations
Combinatoric
a(n)=a(n-1)+gpf(a(n-2))!
a(0)=1
a(1)=1
gpf(n)=greatest prime factor of n
n≥0
5 operations
Prime
a(n)=a(n-1)+lpf(a(n-2))!
a(0)=1
a(1)=1
lpf(n)=least prime factor of n
n≥0
5 operations
Prime
a(n)=a(n-1)+rad(a(n-2))!
a(0)=1
a(1)=1
rad(n)=square free kernel of n
n≥0
5 operations
Prime
a(n)=exp(Λ(a(n-1)))+a(n-2)!
a(0)=1
a(1)=1
Λ(n)=Von Mangoldt's function
n≥0
6 operations
Prime

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