cp's OEIS Frontend

A347161 Sum of squares of odd divisors of n that are < sqrt(n).

%I A347161 #9 Aug 21 2021 13:08:47
%S A347161 0,1,1,1,1,1,1,1,1,1,1,10,1,1,10,1,1,10,1,1,10,1,1,10,1,1,10,1,1,35,1,
%T A347161 1,10,1,26,10,1,1,10,26,1,10,1,1,35,1,1,10,1,26,10,1,1,10,26,50,10,1,
%U A347161 1,35,1,1,59,1,26,10,1,1,10,75,1,10,1,1,35,1,50,10,1,26
%N A347161 Sum of squares of odd divisors of n that are < sqrt(n).
%F A347161 G.f.: Sum_{k>=1} (2*k - 1)^2 * x^(2*k*(2*k - 1)) / (1 - x^(2*k - 1)).
%t A347161 Table[DivisorSum[n, #^2 &, # < Sqrt[n] && OddQ[#] &], {n, 1, 80}]
%t A347161 nmax = 80; CoefficientList[Series[Sum[(2 k - 1)^2 x^(2 k (2 k - 1))/(1 - x^(2 k - 1)), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
%o A347161 (PARI) a(n) = my(r=sqrt(n)); sumdiv(n, d, if ((d%2) && (d<r), d^2)); \\ _Michel Marcus_, Aug 21 2021
%Y A347161 Cf. A001157, A050999, A333805, A333807, A339353, A347162.
%K A347161 nonn
%O A347161 1,12
%A A347161 _Ilya Gutkovskiy_, Aug 20 2021