A333782 G.f.: Sum_{k>=1} (-1)^(k + 1) * k * x^(k^2) / (1 - x^k).

1, 1, 1, -1, 1, -1, 1, -1, 4, -1, 1, 2, 1, -1, 4, -5, 1, 2, 1, -5, 4, -1, 1, -2, 6, -1, 4, -5, 1, 7, 1, -5, 4, -1, 6, -8, 1, -1, 4, 0, 1, -4, 1, -5, 9, -1, 1, -8, 8, 4, 4, -5, 1, -4, 6, 2, 4, -1, 1, -3, 1, -1, 11, -13, 6, -4, 1, -5, 4, 11, 1, -16, 1, -1, 9, -5, 8, -4, 1, -8

Offset: 1

Author

Ilya Gutkovskiy, Apr 05 2020

Keywords

• sign

Comments

Excess of sum of odd divisors of n that are <= sqrt(n) over sum of even divisors of n that are <= sqrt(n).

Crossrefs

Cf. A002129, A066839, A069289, A333781.

Programs

Mathematica

nmax = 80; CoefficientList[Series[Sum[(-1)^(k + 1) k x^(k^2)/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Rest

PARI

a(n) = sumdiv(n, d, if (d^2<=n, if (d%2, d, -d))); \\ Michel Marcus, Apr 05 2020