Sequences

n written in base where place values are positive squares.

a(n) is the largest odd number k such that 9, 11, ..., k are sums of 3 of first n odd primes.

Number of (unordered) ways of writing 2n+1 as a sum of 3 odd primes.

Numbers k such that product of proper divisors of k is <= k; i.e., product of divisors of k is <= k^2.

a(n) = n^prime(n) - prime(n)^n.

First factor in happy factorization of n.

Second factor in happy factorization of n.

Type of happy factorization of n.

Rectangular numbers.

Rhombic numbers.

INVERTi transform of central trinomial coefficients (A002426).

Number of permutations that are 2 "block reversals" away from 12...n.

Number of permutations that are n-2 "block reversals" away from 12...n.

Number of permutations that are n-3 "block reversals" away from 12...n.

Number of permutations that are 3 "block reversals" away from 12...n.

Generalized Euler numbers O_n^+(2).

Modified de Bruijn sequences: max. length of binary necklace in which no n-bit word appears twice.

Least non-divisor of n.

Expansion of (1+x^2)(1+x^4)/((1-x)^2*(1-x^2)*(1-x^3)).

Expansion of (1+x^2)/((1-x)^2*(1-x^3)).

Number of nonsplit type 2 metacyclic 2-groups of order 2^n.

Number of non-Abelian metacyclic groups of order 2^n.

Number of non-Abelian metacyclic groups of order p^n (p odd).

Number of essential graphs with n nodes (in 1-1 correspondence with Markov equivalence classes of acyclic digraphs).

Co-growth function of a certain group.

Co-growth function of a certain group.

Number of irreducible words of length 2n in the free group with generators x,y such that the total degree of x and the total degree of y both equal zero.

Expansion of (x^6-x^5-x^4+2x^2)/((1-x^3)(1-x^2)^2(1-x)).

Slowest increasing sequence with property that a(n) does not divide any term of form a(n+m*a(n)) for any m; this is the slowest increasing "non-difference-divisible" sequence.

Poincaré series [or Poincare series] of Lie algebra associated with a certain braid group.

Poincaré series [or Poincare series] of Lie algebra associated with a certain braid group.

Augmented amicable pairs (smaller member of each pair).

Poincaré series [or Poincare series] of Lie algebra associated with a certain braid group.

Poincaré series (or Poincare series) of Lie algebra associated with a certain braid group.

Poincaré series [or Poincare series] of Lie algebra associated with a certain braid group.

Primes that divide at least one term of Sylvester's sequence s = A000058: s(n+1) = s(n)^2 - s(n) + 1, s(0) = 2.

a(n) = ceiling((n-3)(n-4)/6).

Number of primitive solutions to x + y + z = 0 (mod n).

a(n) is the number of permutations w of 1,2,...,n such that both w and w^{-1} are alternating.

Coordination sequence T1 for Zeolite Code ABW and ATN.

Coordination sequence T1 for Zeolite Code AEI.

Coordination sequence T2 for Zeolite Code AEI.

Coordination sequence T3 for Zeolite Code AEI.

Coordination sequence T1 for Zeolite Code AEL.

Coordination sequence T2 for Zeolite Code AEL.

Coordination sequence T3 for Zeolite Code AEL.

Coordination sequence T1 for Zeolite Code AET.

Coordination sequence T2 for Zeolite Code AET.

Coordination sequence T3 for Zeolite Code AET.

Coordination sequence T4 for Zeolite Code AET.