A111218 d_8(n), tau_8(n), number of ordered factorizations of n as n = rstuvwxy (8-factorizations).

1, 8, 8, 36, 8, 64, 8, 120, 36, 64, 8, 288, 8, 64, 64, 330, 8, 288, 8, 288, 64, 64, 8, 960, 36, 64, 120, 288, 8, 512, 8, 792, 64, 64, 64, 1296, 8, 64, 64, 960, 8, 512, 8, 288, 288, 64, 8, 2640, 36, 288, 64, 288, 8, 960, 64, 960, 64, 64, 8, 2304, 8, 64, 288, 1716, 64, 512, 8

Offset

1,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Formula

G.f.: Sum_{k>=1} tau_7(k)*x^k/(1 - x^k). - Ilya Gutkovskiy, Oct 30 2018

Multiplicative with a(p^e) = binomial(e+7,7). - Amiram Eldar, Sep 13 2020

Mathematica

tau[n_, 1] = 1; tau[n_, k_] := tau[n, k] = Plus @@ (tau[ #, k - 1] & /@ Divisors[n]); Table[ tau[n, 8], {n, 67}] (* Robert G. Wilson v, Nov 02 2005 *)
tau[1, k_] := 1; tau[n_, k_] := Times @@ (Binomial[Last[#]+k-1, k-1]& /@ FactorInteger[n]); Table[tau[n, 8], {n, 1, 100}] (* Amiram Eldar, Sep 13 2020 *)

Prog

(PARI) for(n=1, 100, print1(sumdiv(n, i, sumdiv(i, j, sumdiv(j, k, sumdiv(k, l, sumdiv(l, m, sumdiv(m, x, numdiv(x))))))), ", "))
(PARI) a(n, f=factor(n))=f=f[, 2]; prod(i=1, #f, binomial(f[i]+7, 7)) \\ Charles R Greathouse IV, Oct 28 2017

Crossrefs

Column k=8 of A077592.

Sequence in context: A053596 A141384 A183400 * A339340 A341247 A188275

Adjacent sequences: A111215 A111216 A111217 * A111219 A111220 A111221

Keyword

mult,nonn

Author

Gerald McGarvey, Oct 25 2005

Status

approved