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A050367 Number of ways to factor n into 2 kinds of 2, 3 kinds of 3, ... 33
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
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
KEYWORD
nonn
AUTHOR
Christian G. Bower, Oct 15 1999
STATUS
approved

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Last modified June 20 19:46 EDT 2024. Contains 373532 sequences. (Running on oeis4.)