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%I #17 Jul 04 2018 20:21:25
%S 1,2,3,7,5,12,7,20,15,20,11,45,13,28,30,59,17,66,19,75,42,44,23,150,
%T 40,52,64,105,29,150,31,162,66,68,70,270,37,76,78,250,41,210,43,165,
%U 165,92,47,477,77,180,102,195,53,326,110,350,114,116,59,630,61,124,231
%N Number of ways to factor n into 2 kinds of 2, 3 kinds of 3, ...
%H N. J. A. Sloane, <a href="/A050367/b050367.txt">Table of n, a(n) for n = 1..1000</a>
%F Dirichlet g.f.: Product_{n>=2} 1/(1-1/n^s)^n.
%o (PARI, modeled on _Michael Somos_'s program for A007896, from _N. J. A. Sloane_, May 26 2014)
%o {a(n) = my(A, v, w, m);
%o if(
%o n<1, 0,
%o \\ define unit vector v = [1, 0, 0, ...] of length n
%o v = vector(n, k, k==1);
%o for(k=2, n,
%o m = #digits(n, k) - 1;
%o \\ expand 1/(1-x)^k out far enough
%o A = (1 - x)^ -k + x * O(x^m);
%o \\ w = zero vector of length n
%o w = vector(n);
%o \\ convert A to a vector
%o for(i=0, m, w[k^i] = polcoeff(A, i));
%o \\ build the answer
%o v = dirmul(v, w)
%o );
%o v[n]
%o )
%o };
%o \\ produce the sequence
%o vector(100,n,a(n))
%K nonn
%O 1,2
%A _Christian G. Bower_, Oct 15 1999
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