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

1,12

Comments

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

Links

Table of n, a(n) for n=1..80.

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

Crossrefs

Cf. A002129, A070039, A333782, A333807, A333809.

Sequence in context: A008307 A249694 A192005 * A205592 A099238 A306846

Adjacent sequences: A333807 A333808 A333809 * A333811 A333812 A333813

Keyword

sign

Author

Ilya Gutkovskiy, Apr 05 2020

Status

approved