OFFSET
1,2
FORMULA
a(n) = Sum_{k=1..n} Sum_{d|k, k/d odd} d^n - (d - 1)^n.
a(n) = [x^n] (1/(1 - x)) * Sum_{k>=1} (k^n - (k - 1)^n) * x^k/(1 - x^(2*k)).
a(n) ~ n^n. - Vaclav Kotesovec, Dec 17 2021
MATHEMATICA
a[n_] := Sum[Floor[n/(2*k - 1)]^n, {k, 1, n}]; Array[a, 20] (* Amiram Eldar, Dec 17 2021 *)
PROG
(PARI) a(n) = sum(k=1, n, (n\(2*k-1))^n);
(PARI) a(n) = sum(k=1, n, sumdiv(k, d, k/d%2*(d^n-(d-1)^n)));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Dec 16 2021
STATUS
approved