A344551 a(n) = Sum_{k=1..n} k^floor((n-k)/k).

1, 2, 3, 5, 6, 11, 12, 20, 27, 40, 41, 93, 94, 133, 208, 328, 329, 658, 659, 1217, 1746, 2269, 2270, 5768, 6269, 8330, 12777, 20253, 20254, 45253, 45254, 74390, 113867, 146652, 161211, 401275, 401276, 532367, 886818, 1412574, 1412575, 3053234, 3053235, 4889475, 8396664

Offset: 1

Author

Wesley Ivan Hurt, May 22 2021

Keywords

• nonn

Links

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

Crossrefs

Cf. A002541, A006218, A153485.

Programs

Mathematica

Table[Sum[k^Floor[(n - k)/k], {k, n}], {n, 80}]

PARI

a(n) = sum(k=1, n, k^(n\k-1)); \\ Seiichi Manyama, Jun 06 2021

PARI

my(N=66, x='x+O('x^N)); Vec(sum(k=1, N, x^k*(1-x^k)/(1-k*x^k))/(1-x)) \\ Seiichi Manyama, Jun 06 2021

Formula

a(n) ~ 3^((n - 3 - mod(n,3))/3). - Vaclav Kotesovec, May 28 2021

G.f.: (1/(1 - x)) * Sum_{k>=1} x^k * (1 - x^k)/(1 - k*x^k). - Seiichi Manyama, Jun 06 2021