A345037 a(n) = Sum_{k=1..n} (-k)^(floor(n/k) - 1).

1, 0, 3, -1, 2, 3, 6, -12, 3, 20, 23, -49, -46, 41, 182, -100, -97, -6, -3, -613, 418, 1941, 1944, -5518, -4765, 1364, 10205, 2629, 2632, -1181, -1178, -71404, 7463, 105748, 127245, -233385, -233382, 159813, 868586, -335790, -335787, -853276, -853273, -2689757, 4163818

Offset: 1

Author

Seiichi Manyama, Jun 06 2021

Keywords

• sign

Links

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

Crossrefs

Cf. A344551, A345036.

Programs

Mathematica

a[n_] := Sum[(-k)^(Floor[n/k] - 1), {k, 1, n}]; Array[a, 45] (* Amiram Eldar, Jun 06 2021 *)

PARI

a(n) = sum(k=1, n, (-k)^(n\k-1));

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))

Formula

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

|a(n)| ~ 3^((n - mod(n,3))/3 - 1). - Vaclav Kotesovec, Jun 12 2021