A333809 G.f.: Sum_{k>=1} (-1)^(k + 1) * x^(k*(k + 1)) / (1 - x^k).

0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 2, 0, 1, 1, 1, -1, 2, 0, 1, 0, 1, 0, 2, -1, 1, 2, 1, -1, 2, 0, 2, 0, 1, 0, 2, 0, 1, 0, 1, -1, 3, 0, 1, -1, 1, 1, 2, -1, 1, 0, 2, 0, 2, 0, 1, 0, 1, 0, 3, -1, 2, 0, 1, -1, 2, 2, 1, -2, 1, 0, 3, -1, 2, 0, 1, -1, 2, 0, 1, 0, 2, 0, 2, -2, 1, 2

Offset

1,15

Comments

Number of odd divisors of n that are < sqrt(n) minus number of even divisors of n that are < sqrt(n).

Links

Table of n, a(n) for n=1..90.

Formula

From Ridouane Oudra, Sep 06 2025: (Start)

a(n) = Sum_{d|n, d < sqrt(n)} (-1)^(d+1).

a(n) = A333781(n) - A258998(n).

a(n) = A048272(n) - A348515(n). (End)

Mathematica

nmax = 90; CoefficientList[Series[Sum[(-1)^(k + 1) x^(k (k + 1))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Rest

Crossrefs

Cf. A048272, A056924, A333781, A333805, A333810, A258998, A348515.

Sequence in context: A025916 A212211 A321764 * A306440 A350723 A379679

Adjacent sequences: A333806 A333807 A333808 * A333810 A333811 A333812

Keyword

sign

Author

Ilya Gutkovskiy, Apr 05 2020

Status

approved