Sequences

Numerator of Sum_{k=1..4} k^(-4).

Number of matrices with n columns whose rows do not cover each other. Also antichain covers of an unlabeled n-set.

The noncubes: a(n) = n + floor((n + floor(n^(1/3)))^(1/3)).

A squarefree (or Thue-Morse) ternary sequence: closed under 1->123, 2->13, 3->2. Start with 1.

Largest number not a sum of distinct primes >= prime(n).

Expand sin x / exp x = x-x^2+x^3/3-x^5/30+... and invert nonzero coefficients.

The minimal numbers: sequence A005179 arranged in increasing order.

If k appears, 3k does not.

Numerators of expansion of exp x / sin x.

Largest number not the sum of distinct n-th-order polygonal numbers.

Berstel sequence: a(n+1) = 2*a(n) - 4*a(n-1) + 4*a(n-2).

Liouville's function: parity of number of primes dividing n (with multiplicity).

Multiplicatively perfect numbers j: product of divisors of j is j^2.

a(n) = mu(n) + 1, where mu is the Moebius function.

a(n) = 1 if n is squarefree, otherwise 2.

d_3(n), or tau_3(n), the number of ordered factorizations of n as n = r s t.

d_4(n), or tau_4(n), the number of ordered factorizations of n as n = rstu.

Moebius transform applied twice to sequence 1,0,0,0,....

Moebius transform applied thrice to sequence 1,0,0,0,....

Inverse Moebius transform applied twice to natural numbers.

Inverse Moebius transform applied thrice to natural numbers.

a(n) = Sum_{d|n} phi(d)*mu(n/d).

Moebius transform applied thrice to natural numbers.

Inverse Moebius transform applied twice to squares.

Jordan function J_2(n) (a generalization of phi(n)).

Inverse Moebius transform of Fibonacci numbers 1,1,2,3,5,8,...

Moebius transform of Fibonacci numbers.

Inverse Moebius transform of triangular numbers.

Moebius transform of triangular numbers.

Number of planted trees: all sub-rooted trees from any node are identical; non-root, non-leaf nodes an even distance from the root are of degree 2.

Reversion of g.f. for Fibonacci numbers 1, 1, 2, 3, 5, ....

1 + Sum_{n>=1} a_n x^n = Product_{n>=1} (1-x^n)^prime(n).

Inverse binomial transform of primes.

Binomial transform of primes.

Moebius transform of primes.

Inverse Moebius transform of primes.

Exponentiation of e.g.f. for primes.

Logarithm of e.g.f. for primes.

Knuth's sequence (or Knuth numbers): a(n+1) = 1 + min( 2*a(floor(n/2)), 3*a(floor(n/3)) ).

a(0) = 7, a(1) = 9; for n >= 0, a(2n+1) = a(2n-1)^2 - a(2n-2), a(2n+2) = a(2n)^2 - a(2n+1).

Decimal expansion of 1/17.

Denominators of expansion of exp x / sin x.

Expand cos x / exp x and invert nonzero coefficients.

Number of unlabeled connected series-parallel posets with n nodes.

Number of unlabeled disconnected series-parallel posets with n nodes.

Number of subsequences of [ 1,...,n ] in which each odd number has an even neighbor.

Number of days required to spread gossip to n people.

Number of (j,k): j+k=n, (j,n)=(k,n)=1, j,k squarefree.

Order of group of n X n X n Rubik cube.

Higgs's primes: a(n+1) = smallest prime > a(n) such that a(n+1)-1 divides the product (a(1)...a(n))^2.