A350145 a(n) = Sum_{k=1..n} floor(n/(2*k-1))^n.
1, 4, 28, 257, 3127, 46721, 823673, 16777474, 387440175, 10000060075, 285311849809, 8916117229571, 302875173709313, 11112007094026243, 437893920912819179, 18446744226340554502, 827240262649405488542, 39346408176856882188621
Offset: 1
Keywords
Programs
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Mathematica
a[n_] := Sum[Floor[n/(2*k - 1)]^n, {k, 1, n}]; Array[a, 20] (* Amiram Eldar, Dec 17 2021 *) -
PARI
a(n) = sum(k=1, n, (n\(2*k-1))^n);
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PARI
a(n) = sum(k=1, n, sumdiv(k, d, k/d%2*(d^n-(d-1)^n)));
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