A345106 a(n) = Sum_{k=1..n} k^(n - floor(n/k)).

1, 3, 14, 96, 971, 12015, 184286, 3283598, 67676125, 1572527901, 40843114146, 1170338862814, 36718016941445, 1251213685475261, 46033362584427670, 1818364700307111794, 76762441669319061911, 3448793841153099408185, 164309637864524321789042

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..387

Formula

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

Mathematica

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

Prog

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

Crossrefs

Cf. A076015, A344551, A345107.

Sequence in context: A295110 A136461 A336525 * A276747 A367383 A007470

Adjacent sequences: A345103 A345104 A345105 * A345107 A345108 A345109

Keyword

nonn

Author

Seiichi Manyama, Jun 08 2021

Status

approved