A050368 Number of ways to factor n into distinct factors with 2 kinds of 2, 3 kinds of 3, ...

1, 2, 3, 5, 5, 12, 7, 16, 12, 20, 11, 39, 13, 28, 30, 42, 17, 60, 19, 65, 42, 44, 23, 126, 35, 52, 55, 91, 29, 150, 31, 116, 66, 68, 70, 219, 37, 76, 78, 210, 41, 210, 43, 143, 150, 92, 47, 378, 70, 170, 102, 169, 53, 290, 110, 294, 114, 116, 59, 570, 61, 124, 210

Offset: 1

Author

Christian G. Bower, Oct 15 1999

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A045778, A050367.

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, w=vector(n)); for(i=0, m, w[k^i]=polcoef(p,i)); v=dirmul(v,w)); v} \\ Andrew Howroyd, Oct 27 2019

Formula

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