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

1,2

Links

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

Formula

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

Prog

(PARI, modeled on Michael Somos's program for A007896, from N. J. A. Sloane, May 26 2014)
{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))

Crossrefs

Sequence in context: A333086 A359504 A064011 * A354201 A332210 A192175

Adjacent sequences: A050364 A050365 A050366 * A050368 A050369 A050370

Keyword

nonn

Author

Christian G. Bower, Oct 15 1999

Status

approved