OFFSET
1,2
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
FORMULA
Multiplicative with a(p^e) = (p^(e+1)*(p^(e+1)-1)-(p-1)*(e+1))/(p-1)^2.
Sum_{k=1..n} a(k) ~ c * n^3, where c = ((zeta(2)*zeta(3)^2)/3) * Product_{p prime} (1 + 1/p^2 - 1/p^4 - 1/p^5) = 1.09461730308... . - Amiram Eldar, Oct 28 2022
MATHEMATICA
Table[ Apply[ Plus, DivisorSigma[1, n*Divisors[n]]], {n, 1, 50}]
f[p_, e_] := (p^(e + 1)*(p^(e + 1) - 1) - (p - 1)*(e + 1))/(p - 1)^2; a[1] = 1; a[n_] := Times @@ (f @@@ FactorInteger[n]); Array[a, 100] (* Amiram Eldar, Oct 28 2022 *)
PROG
(Magma) [&+[DivisorSigma(1, n*d):d in Divisors(n)]:n in [1..50]]; // Marius A. Burtea, Sep 15 2019
(PARI) a(n) = sumdiv(n, d, sigma(n*d)); \\ Michel Marcus, Sep 15 2019
CROSSREFS
KEYWORD
mult,easy,nonn
AUTHOR
Vladeta Jovovic, Apr 17 2002
EXTENSIONS
Edited and extended by Robert G. Wilson v, Apr 22 2002
STATUS
approved