A328851 Dirichlet g.f.: Product_{k>=2} 1 / (1 - k^(-s))^(k + 1).

1, 3, 4, 11, 6, 19, 8, 34, 20, 29, 12, 78, 14, 39, 40, 104, 18, 107, 20, 120, 54, 59, 24, 277, 47, 69, 88, 162, 30, 237, 32, 299, 82, 89, 84, 478, 38, 99, 96, 429, 42, 321, 44, 246, 230, 119, 48, 921, 86, 258, 124, 288, 54, 535, 128, 581, 138, 149, 60, 1091

Offset: 1

Author

Ilya Gutkovskiy, Oct 28 2019

Keywords

• nonn

Comments

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

Dirichlet convolution of A001055 with A050367.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..4096

Crossrefs

Cf. A001055, A050367, A328853.

Programs

PARI

seq(n)={my(v=vector(n, k, k==1)); for(k=2, n, my(m=logint(n,k), p=1/(1 - x + O(x*x^m))^(1+k), w=vector(n)); for(i=0, m, w[k^i]=polcoef(p,i)); v=dirmul(v,w)); v} \\ Andrew Howroyd, Oct 28 2019

Formula

a(n) = Sum_{d|n} A001055(n/d) * A050367(d).