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A111220 d_10(n), tau_10(n), number of ordered factorizations of n as n = rstuvwxyza (10-factorizations). 4
1, 10, 10, 55, 10, 100, 10, 220, 55, 100, 10, 550, 10, 100, 100, 715, 10, 550, 10, 550, 100, 100, 10, 2200, 55, 100, 220, 550, 10, 1000, 10, 2002, 100, 100, 100, 3025, 10, 100, 100, 2200, 10, 1000, 10, 550, 550, 100, 10, 7150, 55, 550, 100, 550, 10, 2200, 100 (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_9(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, 10], {n, 55}] (* 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, p, sumdiv(p, x, numdiv(x))))))))), ", "))

(PARI) a(n, f=factor(n))=f=f[, 2]; prod(i=1, #f, binomial(f[i]+9, 9)) \\ Charles R Greathouse IV, Oct 28 2017

CROSSREFS

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

Column k=10 of A077592.

Sequence in context: A201027 A003875 A238017 * A106789 A270012 A219911

Adjacent sequences:  A111217 A111218 A111219 * A111221 A111222 A111223

KEYWORD

mult,nonn

AUTHOR

Gerald McGarvey, Oct 25 2005

STATUS

approved

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Last modified March 24 01:20 EDT 2019. Contains 321444 sequences. (Running on oeis4.)