A344724 a(n) = Sum_{k=1..n} (-1)^(k+1) * floor(n/k)^n.

1, 3, 27, 240, 3094, 45990, 821484, 16711680, 387177517, 9990293423, 285263019633, 8913939911695, 302862111412779, 11111328866154037, 437889173336927557, 18446462747068745474, 827238010832411671962, 39346258082152478030126

Offset

1,2

Links

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

Formula

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

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

a(n) ~ n^n. - Vaclav Kotesovec, May 28 2021

Mathematica

a[n_] := Sum[(-1)^(k + 1) * Quotient[n, k]^n, {k, 1, n}]; Array[a, 18] (* Amiram Eldar, May 27 2021 *)

Prog

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

Crossrefs

Main diagonal of A344726.

Cf. A332469.

Sequence in context: A221769 A065100 A035088 * A381186 A268094 A013708

Adjacent sequences: A344721 A344722 A344723 * A344725 A344726 A344727

Keyword

nonn

Author

Seiichi Manyama, May 27 2021

Status

approved