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 A111306 d_12(n), tau_12(n), number of ordered factorizations of n as n = rstuvwxyzabc (12-factorizations). 6
 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) Adolf Piltz, Ueber das Gesetz, nach welchem die mittlere Darstellbarkeit der natürlichen Zahlen als Produkte einer gegebenen Anzahl Faktoren mit der Grösse der Zahlen wächst, Doctoral Dissertation, Friedrich-Wilhelms-Universität zu Berlin, 1881; the k-th Piltz function tau_k(n) is denoted by phi(n,k) and its recurrence and Dirichlet series appear on p. 6. 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: A003877 A161196 A328531 * 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 June 7 05:20 EDT 2020. Contains 334837 sequences. (Running on oeis4.)