A350125 a(n) = Sum_{k=1..n} k^2 * floor(n/k)^n.

1, 8, 40, 345, 3303, 50225, 833569, 17045934, 388654659, 10039636255, 285508661853, 8924967326015, 302927979357701, 11114722212099135, 437913155876193839, 18447871416712820782, 827249276230172525622, 39347009369000530723017

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..386

Formula

a(n) = Sum_{k=1..n} k^2 * Sum_{d|k} (d^n - (d - 1)^n)/d^2.

a(n) = [x^n] (1/(1 - x)) * Sum_{k>=1} (k^n - (k - 1)^n) * x^k * (1 + x^k)/(1 - x^k)^3.

a(n) ~ n^n. - Vaclav Kotesovec, Dec 16 2021

Mathematica

a[n_] := Sum[k^2 * Floor[n/k]^n, {k, 1, n}]; Array[a, 18] (* Amiram Eldar, Oct 04 2023 *)

Prog

(PARI) a(n) = sum(k=1, n, k^2*(n\k)^n);
(PARI) a(n) = sum(k=1, n, k^2*sumdiv(k, d, (d^n-(d-1)^n)/d^2));

Crossrefs

Cf. A332469, A350109, A350123, A350124, A350128.

Sequence in context: A117083 A007987 A343868 * A096969 A376186 A209829

Adjacent sequences: A350122 A350123 A350124 * A350126 A350127 A350128

Keyword

nonn

Author

Seiichi Manyama, Dec 15 2021

Status

approved