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A111219 d_9(n), tau_9(n), number of ordered factorizations of n as n = rstuvwxyz (9-factorizations). 4
1, 9, 9, 45, 9, 81, 9, 165, 45, 81, 9, 405, 9, 81, 81, 495, 9, 405, 9, 405, 81, 81, 9, 1485, 45, 81, 165, 405, 9, 729, 9, 1287, 81, 81, 81, 2025, 9, 81, 81, 1485, 9, 729, 9, 405, 405, 81, 9, 4455, 45, 405, 81, 405, 9, 1485, 81, 1485, 81, 81, 9, 3645, 9, 81, 405, 3003, 81 (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 PĂ©rez Herrero)

FORMULA

G.f.: Sum_{k>=1} tau_8(k)*x^k/(1 - x^k). - Ilya Gutkovskiy, Oct 30 2018

MATHEMATICA

tau[n_, 1] = 1; tau[n_, k_] := tau[n, k] = Plus @@ (tau[ #, k - 1] & /@ Divisors[n]); Table[ tau[n, 9], {n, 65}] (* Robert G. Wilson v, Nov 02 2005 *)

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, x, numdiv(x)))))))), ", "))

(PARI) a(n, f=factor(n))=f=f[, 2]; prod(i=1, #f, binomial(f[i]+8, 8)) \\ Charles R Greathouse IV, Oct 28 2017

CROSSREFS

Cf. tau_2(n)...tau_6(n): A000005, A007425, A007426, A061200, A034695.

Column k=9 of A077592.

Sequence in context: A097988 A103646 A246314 * A242585 A188276 A152752

Adjacent sequences:  A111216 A111217 A111218 * A111220 A111221 A111222

KEYWORD

mult,nonn

AUTHOR

Gerald McGarvey, Oct 25 2005

STATUS

approved

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Last modified March 19 04:23 EDT 2019. Contains 321311 sequences. (Running on oeis4.)