A328877 Dirichlet g.f.: Product_{k>=2} (1 + k^(-s))^(k - 1).

1, 1, 2, 3, 4, 7, 6, 10, 9, 13, 10, 22, 12, 19, 22, 25, 16, 36, 18, 40, 32, 31, 22, 69, 30, 37, 42, 58, 28, 89, 30, 70, 52, 49, 58, 121, 36, 55, 62, 125, 40, 129, 42, 94, 108, 67, 46, 203, 63, 115, 82, 112, 52, 174, 94, 181, 92, 85, 58, 319, 60, 91, 156, 182

Offset

1,3

Comments

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

Dirichlet convolution of A050368 with A316441.

Links

Table of n, a(n) for n=1..64.

Formula

a(n) = Sum_{d|n} A050368(n/d) * A316441(d).

Prog

(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

Crossrefs

Cf. A050368, A316441, A328853, A328876.

Sequence in context: A255553 A260742 A265228 * A125595 A091202 A106444

Adjacent sequences: A328874 A328875 A328876 * A328878 A328879 A328880

Keyword

nonn

Author

Ilya Gutkovskiy, Oct 29 2019

Status

approved