OFFSET
1,6
LINKS
FORMULA
a(n) = Sum_{d|n, d<n, d odd} d^3.
G.f.: Sum_{k>=1} (2*k-1)^3 * 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^4, where c = (zeta(4)-1)/8 = 0.0102904042... . (End)
EXAMPLE
a(10) = 126; a(10) = Sum_{d|10, d<10, d odd} d^3 = 1^3 + 5^3 = 126.
MATHEMATICA
f[2, e_] := 1; f[p_, e_] := (p^(3*e+3) - 1)/(p^3 - 1); a[1] = 0; a[n_] := Times @@ f @@@ FactorInteger[n] - If[OddQ[n], n^3, 0]; Array[a, 60] (* Amiram Eldar, Oct 11 2023 *)
PROG
(PARI) a(n) = sumdiv(n/2^valuation(n, 2), d, if ((d<n), d^3)); \\ Michel Marcus, Mar 02 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Mar 01 2022
STATUS
approved