A333809 - OEIS

%I #5 Apr 05 2020 23:28:18

%S 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,

%T 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,

%U 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

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

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

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

%Y Cf. A048272, A056924, A333781, A333805, A333810.

%K sign

%O 1,15

%A _Ilya Gutkovskiy_, Apr 05 2020