OFFSET
1,2
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = Sum_{d|n} mu(n/d) * d^4 * tau(d), where mu is the Moebius function A008683.
From Amiram Eldar, May 21 2024: (Start)
Multiplicative with a(p^e) = (e - e/p^4 + 1) * p^(4*e).
Dirichlet g.f.: zeta(s-4)^2/zeta(s).
Sum_{k=1..n} a(k) ~ (n^5/(5*zeta(5))) * (log(n) + 2*gamma - 1/5 - zeta'(5)/zeta(5)), where gamma is Euler's constant (A001620). (End)
MATHEMATICA
f[p_, e_] := (e - e/p^4 + 1) * p^(4*e); 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)*d^4*numdiv(d));
CROSSREFS
KEYWORD
nonn,mult
AUTHOR
Seiichi Manyama, May 17 2024
STATUS
approved