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_10(k)*x^k/(1 - x^k). - Ilya Gutkovskiy, Oct 30 2018
Multiplicative with a(p^e) = binomial(e+10,10). - 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, 11], {n, 55}] (* 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, 11], {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, o, sumdiv(o, p, sumdiv(p, q, sumdiv(q, x, numdiv(x)))))))))), ", "))
(PARI) a(n, f=factor(n))=f=f[, 2]; prod(i=1, #f, binomial(f[i]+10, 10)) \\ Charles R Greathouse IV, Oct 28 2017
KEYWORD
mult,nonn
AUTHOR
Gerald McGarvey, Oct 25 2005
STATUS
approved