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A050367 Number of ways to factor n into 2 kinds of 2, 3 kinds of 3, ... 13
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 (list; graph; refs; listen; history; text; internal format)
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: A117928 A333086 A064011 * A332210 A192175 A294205

Adjacent sequences:  A050364 A050365 A050366 * A050368 A050369 A050370

KEYWORD

nonn

AUTHOR

Christian G. Bower, Oct 15 1999

STATUS

approved

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Last modified April 12 09:25 EDT 2021. Contains 342919 sequences. (Running on oeis4.)