A345100 a(n) = Sum_{k=1..n} k^floor(n/k).

1, 3, 6, 12, 17, 33, 40, 68, 95, 141, 152, 328, 341, 461, 738, 1130, 1147, 2159, 2178, 4068, 5841, 6997, 7020, 18198, 20723, 25001, 38798, 61546, 61575, 137445, 137476, 223252, 342593, 408435, 485376, 1213988, 1214025, 1476549, 2541498, 4202810, 4202851, 8777205

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..5000

Formula

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

a(n) ~ 3^((n - mod(n,3))/3). - Vaclav Kotesovec, Jun 11 2021

Mathematica

a[n_] := Sum[k^Floor[n/k], {k, 1, n}]; Array[a, 40] (* Amiram Eldar, Jun 08 2021 *)

Prog

(PARI) a(n) = sum(k=1, n, k^(n\k));
(PARI) my(N=66, x='x+O('x^N)); Vec(sum(k=1, N, k*x^k*(1-x^k)/(1-k*x^k))/(1-x))

Crossrefs

Cf. A031971, A055225, A344551, A345098.

Sequence in context: A146952 A288570 A038046 * A162845 A239708 A038588

Adjacent sequences: A345097 A345098 A345099 * A345101 A345102 A345103

Keyword

nonn

Author

Seiichi Manyama, Jun 08 2021

Status

approved