A050367 - OEIS

%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