A328876 Dirichlet g.f.: Product_{k>=2} (1 + k^(-s))^(k + 1).

1, 3, 4, 8, 6, 19, 8, 25, 16, 29, 12, 66, 14, 39, 40, 69, 18, 95, 20, 102, 54, 59, 24, 220, 41, 69, 72, 138, 30, 237, 32, 191, 82, 89, 84, 379, 38, 99, 96, 342, 42, 321, 44, 210, 206, 119, 48, 679, 78, 240, 124, 246, 54, 459, 128, 464, 138, 149, 60, 971

Offset: 1

Author

Ilya Gutkovskiy, Oct 29 2019

Keywords

• nonn

Comments

Number of ways to factor n into distinct factors with 3 kinds of 2, 4 kinds of 3, ..., k+1 kinds of k.

Dirichlet convolution of A045778 with A050368.

Crossrefs

Cf. A045778, A050368, A328851, A328877.

Programs

PARI

seq(n)={my(v=vector(n, k, k==1)); for(k=2, n, my(m=logint(n, k), p=(1 + x + O(x*x^m))^(k+1), w=vector(n)); for(i=0, m, w[k^i]=polcoef(p, i)); v=dirmul(v, w)); v} \\ Andrew Howroyd, Oct 29 2019

Formula

a(n) = Sum_{d|n} A045778(n/d) * A050368(d).