cp's OEIS Frontend

A050367 Number of ways to factor n into 2 kinds of 2, 3 kinds of 3, ...

%I A050367 #19 Feb 10 2025 10:32:47
%S A050367 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 A050367 40,52,64,105,29,150,31,162,66,68,70,270,37,76,78,250,41,210,43,165,
%U A050367 165,92,47,477,77,180,102,195,53,326,110,350,114,116,59,630,61,124,231
%N A050367 Number of ways to factor n into 2 kinds of 2, 3 kinds of 3, ...
%H A050367 N. J. A. Sloane, <a href="/A050367/b050367.txt">Table of n, a(n) for n = 1..1000</a>
%F A050367 Dirichlet g.f.: Product_{n>=2} 1/(1-1/n^s)^n.
%o A050367 (PARI) \\ modeled on _Michael Somos_'s program for A007896
%o A050367 {a(n) = my(A, v, w, m);
%o A050367 if(
%o A050367 n<1, 0,
%o A050367 \\ define unit vector v = [1, 0, 0, ...] of length n
%o A050367 v = vector(n, k, k==1);
%o A050367    for(k=2, n,
%o A050367            m = #digits(n, k) - 1;
%o A050367 \\ expand 1/(1-x)^k out far enough
%o A050367            A = (1 - x)^ -k + x * O(x^m);
%o A050367 \\ w = zero vector of length n
%o A050367            w = vector(n);
%o A050367 \\ convert A to a vector
%o A050367            for(i=0, m, w[k^i] = polcoeff(A, i));
%o A050367 \\ build the answer
%o A050367            v = dirmul(v, w)
%o A050367       );
%o A050367 v[n]
%o A050367   )
%o A050367 };
%o A050367 \\ produce the sequence
%o A050367 vector(100,n,a(n)) \\ _N. J. A. Sloane_, May 26 2014
%K A050367 nonn
%O A050367 1,2
%A A050367 _Christian G. Bower_, Oct 15 1999