Sequence Database

A database with 1956199 machine generated integer and decimal sequences.

Displaying result 0-99 of total 1965. [0] [1] [2] [3] [4] ... [19]

Sequence fvggmj41sayzg

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

integer, monotonic, +, A080405 (weak)

a(n)=ω(catalan(n))
catalan(n)=the catalan numbers
ω(n)=number of distinct prime divisors of n
n≥0
3 operations
Prime
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 yi4rbbpqzb14e

0, 0, 1, 1, 2, 3, 4, 3, 4, 4, 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=0.5772... (Euler Gamma)
contfrac(a)=continued fraction of a
n≥0
3 operations
Power

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 hklgggh0c0dk

1, 1, 1, 2, 8, 32, 192, 1152, 9216, more...

integer, monotonic, +, A048855 (weak)

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

Sequence 5jjf1r5kv3ysm

1, 1, 1, 4, 6, 12, 40, 240, 480, 1920, 6912, 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 mksfi0skd5ubo

1, 1, 2, 2, 4, 8, 12, 8, 16, 16, 24, 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 snobetdbfwyue

1, 1, 2, 5, 14, 42, 66, 429, 1430, 4862, 8398, 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

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)

a(n)=∏[catalan(n)]
catalan(n)=the catalan numbers
∏(a)=partial products of a
n≥0
3 operations
Combinatoric

Sequence v3bn1feq0awzj

1, 1, 2, 11, 1575, 1844349560, more...

integer, monotonic, +, A101295 (weak)

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

Sequence giogzovirultj

1, 1, 2, 42, 2674440, more...

integer, monotonic, +, A273399 (weak)

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

Sequence 0lgyp1jmmtjbe

1, 1, 3, 6, 24, 96, 336, 672, 3024, 9072, 35280, 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 eej2jcvjjjfaj

1, 1, 4, 36, 576, 14400, 518400, 25401600, 1625702400, 131681894400, 13168189440000, 1593350922240000, more...

integer, monotonic, +, A001044 (weak)

a(n)=n!²
n≥0
3 operations
Combinatoric
a(n)=n²*a(n-1)
a(0)=1
n≥0
4 operations
Recursive
a(n)=lcm(∏[n²], a(n-1))
a(0)=1
∏(a)=partial products of a
lcm(a,b)=least common multiple
n≥1
5 operations
Recursive
a(n)=∏[C(n, a(n-1))]²
a(0)=1
C(n,k)=binomial coefficient
∏(a)=partial products of a
n≥0
5 operations
Combinatoric
a(n)=lcm(a(n-1), a(n-2))*n²
a(0)=1
a(1)=1
lcm(a,b)=least common multiple
n≥0
6 operations
Recursive

Sequence gki4dwkpk4e2o

1, 1, 6, 720, 3628800, 1307674368000, more...

integer, monotonic, +, A052295 (weak)

a(n)=∑[n]!
∑(a)=partial sums of a
n≥0
3 operations
Combinatoric

Sequence rbtkvpq2vl3yl

1, 1, 14, 4862, 35357670, 4861946401452, more...

integer, monotonic, +, A214441 (weak)

a(n)=catalan(n²)
catalan(n)=the catalan numbers
n≥0
3 operations
Combinatoric

Sequence m11ykhh12hvqb

1, 2, 2, 4, 8, 32, 256, 8192, 2097152, 17179869184, more...

integer, monotonic, +, A000301 (weak)

a(n)=a(n-1)*a(n-2)
a(0)=1
a(1)=2
n≥0
3 operations
Recursive
a(n)=a(n-1)²/a(n-3)
a(0)=1
a(1)=2
a(2)=2
n≥0
4 operations
Recursive
a(n)=lcm(floor(a(n-1))*a(n-2), 2)
a(0)=1
a(1)=2
lcm(a,b)=least common multiple
n≥0
6 operations
Recursive
a(n)=a(n-1)*φ(2*a(n-2))
a(0)=1
a(1)=2
ϕ(n)=number of relative primes (Euler's totient)
n≥0
6 operations
Prime
a(n)=2^Ω(a(n-2))*a(n-1)
a(0)=1
a(1)=2
Ω(n)=number of prime divisors of n
n≥0
6 operations
Prime

Sequence xlbwvtrjorhbf

1, 6, 24, 5040, 720, 479001600, 40320, 1307674368000, 6227020800, more...

integer, non-monotonic, +, A184388 (weak)

a(n)=σ(n)!
σ(n)=divisor sum of n
n≥1
3 operations
Prime
a(n)=σ(τ(2^n))!
τ(n)=number of divisors of n
σ(n)=divisor sum of n
n≥0
6 operations
Prime
a(n)=σ(Ω(2^n))!
Ω(n)=number of prime divisors of n
σ(n)=divisor sum of n
n≥1
6 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)

a(n)=C(9, n)
C(n,k)=binomial coefficient
n≥0
3 operations
Combinatoric

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 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)

a(n)=C(11, n)
C(n,k)=binomial coefficient
n≥0
3 operations
Combinatoric

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 lv2nwwf4t1i1n

2, 2, 4, 64, 16777216, more...

integer, monotonic, +, A050923 (weak)

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

Sequence cf4w3ht214ouk

3, 3, 9, 729, 282429536481, more...

integer, monotonic, +, A100731 (weak)

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

Sequence avqbvzm2whb3o

4, 4, 6, 20, 4845, more...

integer, monotonic, +, A143391 (weak)

a(n)=C(a(n-1), n)
a(0)=4
C(n,k)=binomial coefficient
n≥0
3 operations
Combinatoric

Sequence zncicw2rzynzl

4, 4, 16, 4096, 281474976710656, more...

integer, monotonic, +, A101407 (weak)

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

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

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 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 v5uzdbzivs0rk

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

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

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
a(n)=Ω(rad(∑[catalan(n)]))
catalan(n)=the catalan numbers
∑(a)=partial sums of a
rad(n)=square free kernel of n
Ω(n)=number of prime divisors of n
n≥0
5 operations
Prime

Sequence qi23qvvwo5tpf

0, 1, 1, 4, 25, 841, 749956, 563696135209, more...

integer, monotonic, +, A014253 (weak)

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

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 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)

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 ebi3l0wd03hm

0, 2, 4, 8, 7, more...

integer, non-monotonic, +, A225746 (weak)

a(n)=Ω(σ(n)!)
σ(n)=divisor sum of n
Ω(n)=number of prime divisors of n
n≥1
4 operations
Prime

Sequence c4xzl3s122vlc

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

integer, non-monotonic, +, A021036 (weak)

a(n)=de[1/32]
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)

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

Sequence 31ttrcbj4qghc

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

integer, non-monotonic, +-, A210245 (weak)

a(n)=λ(ceil(exp(n)))
λ(n)=Liouville's function
n≥0
4 operations
Prime

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 iueowioqr3wob

1, 0, 4, 1, 9, 16, 100, 8649, 74666881, more...

integer, non-monotonic, +, A143763 (weak)

a(n)=(n-a(n-1))²
a(0)=1
n≥0
4 operations
Recursive
a(n)=((n-a(n-1))*λ(n))²
a(0)=1
λ(n)=Liouville's function
n≥0
7 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

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 4vhfza5ujnof

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

integer, non-monotonic, +, A226912 (weak)

a(n)=μ(composite(catalan(n)))
catalan(n)=the catalan numbers
composite(n)=nth composite number
μ(n)=Möbius function
n≥0
4 operations
Prime

Sequence weylhshnpi1bl

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

integer, monotonic, +, A061603 (weak)

a(n)=C(n, 9)!
C(n,k)=binomial coefficient
n≥0
4 operations
Combinatoric

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
gpf(n)=greatest prime factor of n
n≥0
5 operations
Prime
a(n)=pt(τ(rad(catalan(n))))
catalan(n)=the catalan numbers
rad(n)=square free kernel of n
τ(n)=number of divisors of n
pt(n)=Pascals triangle by rows
n≥0
5 operations
Prime

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 yottiq432kyvc

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

integer, monotonic, +, A305855 (weak)

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

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 p3lxpydtsf03k

1, 1, 1, 20, 10626, 190578024, 189492294437160, more...

integer, monotonic, +, A086687 (weak)

a(n)=C(n!, n)
C(n,k)=binomial coefficient
n≥0
4 operations
Combinatoric

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

Sequence fvdy305ryz0bg

1, 1, 2, 3, 8, 40323, more...

integer, monotonic, +, A075849 (weak)

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

Sequence oeleeusokgknk

1, 1, 2, 3, 15, 176, 526823, 476715857290, more...

integer, monotonic, +, A180723 (weak)

a(n)=P(P(P(n)))
P(n)=partition numbers
n≥0
4 operations
Combinatoric

Sequence 2425ln1afs3j

1, 1, 2, 6, 18, 54, 216, 864, 3456, more...

integer, monotonic, +, A094590 (weak)

a(n)=∏[ω(catalan(n))]
catalan(n)=the catalan numbers
ω(n)=number of distinct prime divisors of n
∏(a)=partial products of a
n≥2
4 operations
Prime
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
∏(a)=partial products of a
n≥2
5 operations
Prime

Sequence 2lothmgbktvpc

1, 1, 2, 12, 576, 1658880, 16511297126400, more...

integer, monotonic, +, A052129 (weak)

a(n)=n*a(n-1)²
a(0)=1
n≥0
4 operations
Recursive
a(n)=n*lcm(a(n-1)², a(n-2))
a(0)=1
a(1)=1
lcm(a,b)=least common multiple
n≥0
6 operations
Recursive
a(n)=lcm(n, n*a(n-1)*a(n-1))
a(0)=1
lcm(a,b)=least common multiple
n≥0
7 operations
Recursive
a(n)=n*(a(n-1)*λ(n))²
a(0)=1
λ(n)=Liouville's function
n≥0
7 operations
Prime

Sequence eetfx4zli1x5f

1, 1, 2, 12, 65520, more...

integer, monotonic, +, A038081 (weak)

a(n)=Δ[2^a(n-1)]
a(0)=0
Δ(a)=differences of a
n≥0
4 operations
Recursive

Sequence g3sbelgslg5qm

1, 1, 2, 20, 2800, 16464000, 12778698240000, more...

integer, monotonic, +, A055746 (weak)

a(n)=∏[∏[catalan(n)]]
catalan(n)=the catalan numbers
∏(a)=partial products of a
n≥0
4 operations
Combinatoric

Sequence 4apabs44dhrnn

1, 1, 2, 24, 6912, 238878720, more...

integer, monotonic, +, A055462 (weak)

a(n)=∏[∏[n!]]
∏(a)=partial products of a
n≥0
4 operations
Combinatoric

Sequence 2asurag0xcunj

1, 1, 3, 4, 9, 6, 49, more...

integer, non-monotonic, +, A062319 (weak)

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

Sequence easehbxwiybnb

1, 1, 3, 7, 29, 151, 1069, 9887, 115891, 1666421, more...

integer, monotonic, +, A082096 (weak)

a(n)=p(a(n-1)+a(n-2))
a(0)=1
a(1)=1
p(n)=nth prime
n≥0
4 operations
Prime

Sequence 0qi4lkpxvuq1m

1, 1, 3, 9, 21, 63, more...

integer, monotonic, +, A073947 (weak)

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

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 q0tuwlti11i

1, 1, 4, 27, 625, 16807, 1771561, 170859375, 54875873536, 19683000000000, more...

integer, monotonic, +, A133018 (weak)

a(n)=P(n)^n
P(n)=partition numbers
n≥0
4 operations
Combinatoric
a(n)=rad(P(n))^n
P(n)=partition numbers
rad(n)=square free kernel of n
n≥0
5 operations
Prime
a(n)=exp(n*log(P(n)))
P(n)=partition numbers
n≥0
6 operations
Combinatoric
a(n)=P(Ω(2^n))^n
Ω(n)=number of prime divisors of n
P(n)=partition numbers
n≥0
7 operations
Prime

Sequence gn1zto4jttc0i

1, 1, 4, 108, 27648, 86400000, 4031078400000, more...

integer, monotonic, +, A002109 (weak)

a(n)=∏[n^n]
∏(a)=partial products of a
n≥0
4 operations
Power
a(n)=n^n*a(n-1)
a(0)=1
n≥0
5 operations
Recursive

Sequence qvwc5s4akdutf

1, 1, 4, 144, 82944, 1194393600, 619173642240000, more...

integer, monotonic, +, A055209 (weak)

a(n)=∏[n!]²
∏(a)=partial products of a
n≥0
4 operations
Combinatoric
a(n)=∏[n²]*a(n-1)
a(0)=1
∏(a)=partial products of a
n≥1
5 operations
Recursive
a(n)=∏[∏[n²]/n²]
∏(a)=partial products of a
n≥1
7 operations
Power

Sequence zr1qgt34dxd1k

1, 1, 4, 144, 331776, 2751882854400, more...

integer, monotonic, +, A030450 (weak)

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

Sequence gs32n1ldzjxzj

1, 1, 4, 216, 331776, 24883200000, more...

integer, monotonic, +, A036740 (weak)

a(n)=n!^n
n≥0
4 operations
Combinatoric

Sequence hnkeu5zkb1ww

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

integer, non-monotonic, +, A154801 (weak)

a(n)=de[37/32]
de(a)=decimal expansion of a
n≥0
4 operations
Arithmetic

Sequence rgwqgujsinyxj

1, 1, 6, 84, 1820, 53130, 1947792, 85900584, 4426165368, 260887834350, 17310309456440, 1276749965026536, more...

integer, monotonic, +, A014062 (weak)

a(n)=C(n², n)
C(n,k)=binomial coefficient
n≥0
4 operations
Combinatoric

Sequence jxrlwiwgecd5l

1, 1, 7, 40, 511, 3906, 138811, more...

integer, monotonic, +, A062727 (weak)

a(n)=σ(n^n)
σ(n)=divisor sum of n
n≥0
4 operations
Prime

Sequence 4vmaeocr032bk

1, 1, 8, 125, 2744, 74088, 2299968, 78953589, 2924207000, 114933031928, 4738245926336, 203152294091656, more...

integer, monotonic, +, A033536 (weak)

a(n)=catalan(n)^3
catalan(n)=the catalan numbers
n≥0
4 operations
Combinatoric

Sequence rdwfm3iepmw0c

1, 1, 8, 216, 13824, 1728000, 373248000, 128024064000, 65548320768000, more...

integer, monotonic, +, A000442 (weak)

a(n)=n!^3
n≥0
4 operations
Combinatoric
a(n)=n^3*a(n-1)
a(0)=1
n≥0
5 operations
Recursive

Sequence wiuqkwgxn3eck

1, 1, 8, 729, 1048576, 30517578125, more...

integer, monotonic, +, A023813 (weak)

a(n)=n^∑[n]
∑(a)=partial sums of a
n≥0
4 operations
Power

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