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A050367 Number of ways to factor n into 2 kinds of 2, 3 kinds of 3, ... 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 (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: A139317 A117928 A064011 * A192175 A294205 A059459

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 October 18 08:08 EDT 2019. Contains 328146 sequences. (Running on oeis4.)