OFFSET
1,6
LINKS
FORMULA
a(n) = Sum_{d|n, d<n, d odd} d^6.
G.f.: Sum_{k>=1} (2*k-1)^6 * x^(4*k-2) / (1 - x^(2*k-1)). - Ilya Gutkovskiy, Mar 02 2022
Sum_{k=1..n} a(k) ~ c * n^7, where c = (zeta(7)-1)/14 = 0.0005963769... . - Amiram Eldar, Oct 11 2023
EXAMPLE
a(10) = 15626; a(10) = Sum_{d|10, d<10, d odd} d^6 = 1^6 + 5^6 = 15626.
MATHEMATICA
f[2, e_] := 1; f[p_, e_] := (p^(6*e+6) - 1)/(p^6 - 1); a[1] = 0; a[n_] := Times @@ f @@@ FactorInteger[n] - If[OddQ[n], n^6, 0]; Array[a, 60] (* Amiram Eldar, Oct 11 2023 *)
Table[Total[Select[Most[Divisors[n]], OddQ]^6], {n, 50}] (* Harvey P. Dale, Sep 15 2024 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Mar 01 2022
STATUS
approved