OFFSET
1,2
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = Sum_{d|n} mu(n/d) * (n/d) * sigma_5(d).
From Amiram Eldar, May 21 2024: (Start)
Multiplicative with a(p^e) = (p^(5*e+5) - p^(5*e+1) + p - 1)/(p^5-1).
Dirichlet g.f.: zeta(s)*zeta(s-5)/zeta(s-1).
Sum_{k=1..n} a(k) ~ c * n^6 / 6, where c = zeta(6)/zeta(5) = 0.981112769... . (End)
a(n) = Sum_{1 <= x_1, x_2, x_3, x_4 <= n} ( gcd(x_1, x_2, x_3, n)/gcd(x_1, x_2, x_3, x_4, n) )^4. - Seiichi Manyama, May 25 2024
MATHEMATICA
f[p_, e_] := (p^(5*e+5) - p^(5*e+1) + p - 1)/(p^5-1); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, May 21 2024 *)
PROG
(PARI) a(n) = sumdiv(n, d, moebius(n/d)*n/d*sigma(d, 5));
CROSSREFS
KEYWORD
nonn,mult
AUTHOR
Seiichi Manyama, May 18 2024
STATUS
approved