OFFSET
1,6
LINKS
FORMULA
a(n) = Sum_{d|n, d<n, d odd} d^7.
G.f.: Sum_{k>=1} (2*k-1)^7 * 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^8, where c = (zeta(8)-1)/16 = 0.0002548347... . (End)
EXAMPLE
a(10) = 78126; a(10) = Sum_{d|10, d<10, d odd} d^7 = 1^7 + 5^7 = 78126.
MATHEMATICA
f[2, e_] := 1; f[p_, e_] := (p^(7*e+7) - 1)/(p^7 - 1); a[1] = 0; a[n_] := Times @@ f @@@ FactorInteger[n] - If[OddQ[n], n^7, 0]; Array[a, 60] (* Amiram Eldar, Oct 11 2023 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Mar 01 2022
STATUS
approved