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A111306 d_12(n), tau_12(n), number of ordered factorizations of n as n = rstuvwxyzabc (12-factorizations). 5
1, 12, 12, 78, 12, 144, 12, 364, 78, 144, 12, 936, 12, 144, 144, 1365, 12, 936, 12, 936, 144, 144, 12, 4368, 78, 144, 364, 936, 12, 1728, 12, 4368, 144, 144, 144, 6084, 12, 144, 144, 4368, 12, 1728, 12, 936, 936, 144, 12, 16380, 78, 936, 144, 936, 12, 4368, 144 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Enrique Pérez Herrero)

FORMULA

G.f.: Sum_{k>=1} tau_11(k)*x^k/(1 - x^k). - Ilya Gutkovskiy, Oct 30 2018

MATHEMATICA

tau[k_, 1]:=1; tau[k_, n_]:=Times@@(Binomial[#+k-1, k-1]&/@FactorInteger[n][[All, 2]]); Table[tau[12, n], {n, 1000}] (* Enrique Pérez Herrero, Jan 17 2013 *)

PROG

(PARI) for(n=1, 100, print1(sumdiv(n, i, sumdiv(i, j, sumdiv(j, k, sumdiv(k, l, sumdiv(l, m, sumdiv(m, o, sumdiv(o, p, sumdiv(p, q, sumdiv(q, r, sumdiv(r, x, numdiv(x))))))))))), ", "))

(PARI) a(n, f=factor(n))=f=f[, 2]; prod(i=1, #f, binomial(f[i]+11, 11)) \\ Charles R Greathouse IV, Oct 28 2017

CROSSREFS

Cf. tau_2(n)...tau_6(n): A000005, A007425, A007426, A061200, A034695, tau_7(n)...tau_11(n): A111217-A111221.

Column k=12 of A077592.

Sequence in context: A147833 A003877 A161196 * A151777 A143478 A219400

Adjacent sequences:  A111303 A111304 A111305 * A111307 A111308 A111309

KEYWORD

mult,nonn

AUTHOR

Gerald McGarvey, Nov 02 2005

STATUS

approved

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Last modified March 23 05:36 EDT 2019. Contains 321422 sequences. (Running on oeis4.)