%I #6 Apr 05 2020 23:28:04

%S 0,1,1,1,1,1,1,1,1,1,1,4,1,1,4,1,1,4,1,1,4,1,1,4,1,1,4,1,1,9,1,1,4,1,

%T 6,4,1,1,4,6,1,4,1,1,9,1,1,4,1,6,4,1,1,4,6,8,4,1,1,9,1,1,11,1,6,4,1,1,

%U 4,13,1,4,1,1,9,1,8,4,1,6,4,1,1,11,6,1,4,1,1,18

%N Sum of odd divisors of n that are < sqrt(n).

%F G.f.: Sum_{k>=1} (2*k - 1) * x^(2*k*(2*k - 1)) / (1 - x^(2*k - 1)).

%t Table[DivisorSum[n, # &, # < Sqrt[n] && OddQ[#] &], {n, 1, 90}]

%t nmax = 90; CoefficientList[Series[Sum[(2 k - 1) x^(2 k (2 k - 1))/(1 - x^(2 k - 1)), {k, 1, nmax}], {x, 0, nmax}], x] // Rest

%Y Cf. A000593, A069289, A070039, A333805, A333808, A333810.

%K nonn

%O 1,12

%A _Ilya Gutkovskiy_, Apr 05 2020