OFFSET
1,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..10000
FORMULA
Multiplicative with a(p^e) = (p^(6*e + 3) + 1)/(p^3 + 1). - Amiram Eldar, Sep 13 2020
Sum_{k>=1} 1/a(k) = 1.019347996519986873084210965032965644185467985307512751244884310846924559959... - Vaclav Kotesovec, Sep 24 2020
Sum_{k=1..n} a(k) ~ c * n^7, where c = 90*zeta(7)/(7*Pi^4) = 0.133093... . - Amiram Eldar, Oct 30 2022
From Seiichi Manyama, May 18 2024: (Start)
a(n) = Sum_{1 <= x_1, x_2, x_3 <= n} ( n/gcd(x_1, x_2, x_3, n) )^3.
a(n) = Sum_{d|n} mu(n/d) * (n/d)^3 * sigma_6(d). (End)
MAPLE
with(numtheory): a:=n->sigma[6](n^2)/sigma[3](n^2): seq(a(n), n=1..30); # Muniru A Asiru, Oct 09 2018
MATHEMATICA
Table[DivisorSigma[6, n^2]/DivisorSigma[3, n^2], {n, 30}] (* Harvey P. Dale, May 02 2012 *)
f[p_, e_] := (p^(6*e + 3) + 1)/(p^3 + 1); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 30] (* Amiram Eldar, Sep 13 2020 *)
PROG
(PARI) a(n)=sumdiv(n^2, d, d^6)/sumdiv(n^2, d, d^3)
(PARI) a(n) = sigma(n^2, 6)/sigma(n^2, 3); \\ Michel Marcus, Oct 09 2018
CROSSREFS
KEYWORD
nonn,mult
AUTHOR
Benoit Cloitre, Jun 21 2003
STATUS
approved