A345094 a(n) = Sum_{k=1..n} floor(n/k)^(floor(n/k) - 1).

1, 3, 11, 68, 630, 7790, 117664, 2097224, 43046801, 1000000643, 25937425245, 743008378547, 23298085130341, 793714773371879, 29192926025508929, 1152921504608944840, 48661191875668966346, 2185911559738739586562, 104127350297911284587436

Offset

1,2

Links

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

Formula

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

Mathematica

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

Prog

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

Crossrefs

Cf. A060946, A262843, A344551, A345030, A345098.

Sequence in context: A342436 A342394 A342370 * A074504 A126115 A342057

Adjacent sequences: A345091 A345092 A345093 * A345095 A345096 A345097

Keyword

nonn

Author

Seiichi Manyama, Jun 07 2021

Status

approved