A345107 a(n) = Sum_{k=1..n} (-k)^(n - floor(n/k)).

1, -1, 14, -86, 955, -11851, 183800, -3273914, 67643293, -1571615577, 40838683608, -1170198385960, 36717193651461, -1251181160936837, 46033142685018824, -1818354391006060750, 76762360864947676457, -3448789505696369210193

Offset: 1

Author

Seiichi Manyama, Jun 08 2021

Keywords

• sign

Links

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

Crossrefs

Cf. A345037, A345106.

Programs

Mathematica

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

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))))

Formula

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