A050368 - OEIS

%I #13 May 20 2021 09:37:25

%S 1,2,3,5,5,12,7,16,12,20,11,39,13,28,30,42,17,60,19,65,42,44,23,126,

%T 35,52,55,91,29,150,31,116,66,68,70,219,37,76,78,210,41,210,43,143,

%U 150,92,47,378,70,170,102,169,53,290,110,294,114,116,59,570,61,124,210

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

%H Andrew Howroyd, <a href="/A050368/b050368.txt">Table of n, a(n) for n = 1..1000</a>

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

%o (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

%Y Cf. A045778, A050367.

%K nonn

%O 1,2

%A _Christian G. Bower_, Oct 15 1999