A356240 a(n) = Sum_{k=1..n} (k-1)^n * Sum_{j=1..floor(n/k)} j^n.

0, 1, 9, 114, 1332, 25404, 395460, 9724901, 207584371, 6120938951, 151737244257, 5932533980409, 168400694345669, 7145593797561899, 260681076993636793, 12410128414690753548, 473029927456547840472, 27572016889372245275679

Offset

1,3

Links

Table of n, a(n) for n=1..18.

Formula

a(n) = Sum_{k=1..n} k^n * (sigma_0(k) - floor(n/k)^n) = A356239(n) - A356238(n).

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

Mathematica

a[n_] := Sum[(k - 1)^n * Sum[j^n, {j, 1, Floor[n/k]}], {k, 1, n}]; Array[a, 18] (* Amiram Eldar, Jul 30 2022 *)

Prog

(PARI) a(n) = sum(k=1, n, (k-1)^n*sum(j=1, n\k, j^n));
(PARI) a(n) = sum(k=1, n, k^n*(sigma(k, 0)-(n\k)^n));
(PARI) a(n) = sum(k=1, n, k^n*sumdiv(k, d, (1-1/d)^n));

Crossrefs

Cf. A356131, A356238, A356239, A356244.

Sequence in context: A243676 A012116 A362576 * A157551 A157570 A223499

Adjacent sequences: A356237 A356238 A356239 * A356241 A356242 A356243

Keyword

nonn

Author

Seiichi Manyama, Jul 30 2022

Status

approved