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%I #4 Apr 05 2020 23:28:25
%S 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,
%T 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,
%U 1,-3,1,-1,11,-5,6,-4,1,-5,4,11,1,-16,1,-1,9,-5,8,-4,1,-8
%N G.f.: Sum_{k>=1} (-1)^(k + 1) * k * x^(k*(k + 1)) / (1 - x^k).
%C Excess of sum of odd divisors of n that are < sqrt(n) over sum of even divisors of n that are < sqrt(n).
%t nmax = 80; CoefficientList[Series[Sum[(-1)^(k + 1) k x^(k (k + 1))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
%Y Cf. A002129, A070039, A333782, A333807, A333809.
%K sign
%O 1,12
%A _Ilya Gutkovskiy_, Apr 05 2020