OFFSET
1,6
LINKS
FORMULA
a(n) = Sum_{d|n, d<n, d odd} d^8.
G.f.: Sum_{k>=1} (2*k-1)^8 * x^(4*k-2) / (1 - x^(2*k-1)). - Ilya Gutkovskiy, Mar 02 2022
From Amiram Eldar, Oct 11 2023: (Start)
Sum_{k=1..n} a(k) ~ c * n^9, where c = (zeta(9)-1)/18 = 0.0001115773... . (End)
EXAMPLE
a(10) = 390626; a(10) = Sum_{d|10, d<10, d odd} d^8 = 1^8 + 5^8 = 390626.
MATHEMATICA
Table[Total[Select[Most[Divisors[n]], OddQ]^8], {n, 45}] (* Harvey P. Dale, Aug 07 2022 *)
f[2, e_] := 1; f[p_, e_] := (p^(8*e+8) - 1)/(p^8 - 1); a[1] = 0; a[n_] := Times @@ f @@@ FactorInteger[n] - If[OddQ[n], n^8, 0]; Array[a, 60] (* Amiram Eldar, Oct 11 2023 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Mar 01 2022
STATUS
approved