OFFSET
1,2
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = Sum_{1 <= x_1, x_2, x_3, x_4, x_5 <= n} ( n/gcd(x_1, x_2, x_3, x_4, x^5, n) )^5.
a(n) = Sum_{d|n} mu(n/d) * (n/d)^5 * sigma_10(d).
From Amiram Eldar, May 25 2024: (Start)
Multiplicative with a(p^e) = (p^(10*e+5) + 1)/(p^5 + 1).
Dirichlet g.f.: zeta(s)*zeta(s-10)/zeta(s-5).
Sum_{k=1..n} a(k) ~ c * n^11 / 11, where c = zeta(11)/zeta(6) = 0.9834383562... . (End)
MATHEMATICA
f[p_, e_] := (p^(10*e+5) + 1)/(p^5 + 1); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 20] (* Amiram Eldar, May 25 2024 *)
PROG
(PARI) a(n) = sigma(n^2, 10)/sigma(n^2, 5);
(PARI) a(n) = sumdiv(n, d, moebius(n/d)*(n/d)^5*sigma(d, 10));
CROSSREFS
KEYWORD
nonn,mult
AUTHOR
Seiichi Manyama, May 25 2024
STATUS
approved