A345036 a(n) = Sum_{k=1..n} (-n)^(floor(n/k) - 1).

1, -1, 11, -66, 623, -7743, 117695, -2097676, 43046069, -999989915, 25937439347, -743008621122, 23298084749141, -793714765727191, 29192926036832303, -1152921504875220776, 48661191875256608663, -2185911559727678466189, 104127350297928222613599

Offset: 1

Author

Seiichi Manyama, Jun 06 2021

Keywords

• sign

Links

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

Crossrefs

Diagonal of A345033.

Cf. A344820, A345030, A345037.

Programs

Mathematica

a[n_] := Sum[(-n)^(Floor[n/k] - 1), {k, 1, n}]; Array[a, 20] (* Amiram Eldar, Jun 06 2021 *)

PARI

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

Formula

a(n) = [x^n] (1/(1 - x)) * Sum_{k>=1} x^k * (1 - x^k)/(1 + n*x^k).