A345098 a(n) = Sum_{k=1..n} floor(n/k)^floor(n/k).

1, 5, 29, 262, 3132, 46690, 823578, 16777484, 387420781, 10000003165, 285311673777, 8916100495209, 302875106639207, 11112006826381861, 437893890381686113, 18446744073726332260, 827240261886353544822, 39346408075296925042900

Offset

1,2

Links

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

Formula

G.f.: (1/(1 - x)) * Sum_{j>=1} Sum_{k>=1} (k*x^j)^k * (1 - x^j).

a(n) ~ n^n. - Vaclav Kotesovec, Jun 11 2021

Mathematica

a[n_] := Sum[Floor[n/k]^Floor[n/k], {k, 1, n}]; Array[a, 20] (* Amiram Eldar, Jun 08 2021 *)

Prog

(PARI) a(n) = sum(k=1, n, (n\k)^(n\k));
(PARI) my(N=20, x='x+O('x^N)); Vec(sum(j=1, N, (1-x^j)*sum(k=1, N, (k*x^j)^k))/(1-x))

Crossrefs

Cf. A062796, A345094, A345100.

Sequence in context: A215867 A342423 A342449 * A144015 A326986 A228387

Adjacent sequences: A345095 A345096 A345097 * A345099 A345100 A345101

Keyword

nonn

Author

Seiichi Manyama, Jun 07 2021

Status

approved