A333810 G.f.: Sum_{k>=1} (-1)^(k + 1) * k * x^(k*(k + 1)) / (1 - x^k).

0, 1, 1, 1, 1, -1, 1, -1, 1, -1, 1, 2, 1, -1, 4, -1, 1, 2, 1, -5, 4, -1, 1, -2, 1, -1, 4, -5, 1, 7, 1, -5, 4, -1, 6, -2, 1, -1, 4, 0, 1, -4, 1, -5, 9, -1, 1, -8, 1, 4, 4, -5, 1, -4, 6, 2, 4, -1, 1, -3, 1, -1, 11, -5, 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, A070039, A333782, A333807, A333809.

Programs

Mathematica

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