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

1, 2, 3, 7, 5, 12, 7, 20, 15, 20, 11, 45, 13, 28, 30, 59, 17, 66, 19, 75, 42, 44, 23, 150, 40, 52, 64, 105, 29, 150, 31, 162, 66, 68, 70, 270, 37, 76, 78, 250, 41, 210, 43, 165, 165, 92, 47, 477, 77, 180, 102, 195, 53, 326, 110, 350, 114, 116, 59, 630, 61, 124, 231

Offset: 1

Author

Christian G. Bower, Oct 15 1999

Keywords

• nonn

Links

• N. J. A. Sloane, Table of n, a(n) for n = 1..1000

Programs

PARI

\\ modeled on Michael Somos's program for A007896
{a(n) = my(A, v, w, m);
if(
n<1, 0,
\\ define unit vector v = [1, 0, 0, ...] of length n
v = vector(n, k, k==1);
   for(k=2, n,
           m = #digits(n, k) - 1;
\\ expand 1/(1-x)^k out far enough
           A = (1 - x)^ -k + x * O(x^m);
\\ w = zero vector of length n
           w = vector(n);
\\ convert A to a vector
           for(i=0, m, w[k^i] = polcoeff(A, i));
\\ build the answer
           v = dirmul(v, w)
      );
v[n]
  )
};
\\ produce the sequence
vector(100,n,a(n)) \\ N. J. A. Sloane, May 26 2014

Formula

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