A350109 a(n) = Sum_{k=1..n} k * floor(n/k)^n.

1, 6, 32, 295, 3201, 48321, 828323, 16910106, 388005909, 10019717653, 285409876785, 8920506515453, 302901435774351, 11113364096436947, 437903477186179875, 18447307498823123948, 827244767844150424228, 39346708569526147402819

Offset

1,2

Links

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

Formula

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

a(n) = [x^n] (1/(1 - x)) * Sum_{k>=1} (k^n - (k - 1)^n) * x^k/(1 - x^k)^2.

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

Mathematica

a[n_] := Sum[k * Floor[n/k]^n, {k, 1, n}]; Array[a, 18] (* Amiram Eldar, Dec 14 2021 *)

Prog

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

Crossrefs

Main diagonal of A350106.

Cf. A319194, A332469.

Sequence in context: A183681 A326985 A350485 * A185386 A368287 A276351

Adjacent sequences: A350106 A350107 A350108 * A350110 A350111 A350112

Keyword

nonn

Author

Seiichi Manyama, Dec 14 2021

Status

approved