A347172 - OEIS

%I #4 Aug 22 2021 00:17:16

%S 0,1,1,1,1,1,1,1,1,1,1,82,1,1,82,1,1,82,1,1,82,1,1,82,1,1,82,1,1,707,

%T 1,1,82,1,626,82,1,1,82,626,1,82,1,1,707,1,1,82,1,626,82,1,1,82,626,

%U 2402,82,1,1,707,1,1,2483,1,626,82,1,1,82,3027,1,82,1,1,707

%N Sum of 4th powers of odd divisors of n that are < sqrt(n).

%F G.f.: Sum_{k>=1} (2*k - 1)^4 * x^(2*k*(2*k - 1)) / (1 - x^(2*k - 1)).

%t Table[DivisorSum[n, #^4 &, # < Sqrt[n] && OddQ[#] &], {n, 1, 75}]

%t nmax = 75; CoefficientList[Series[Sum[(2 k - 1)^4 x^(2 k (2 k - 1))/(1 - x^(2 k - 1)), {k, 1, nmax}], {x, 0, nmax}], x] // Rest

%Y Cf. A001159, A051001, A333805, A333807, A347142, A347161, A347162.

%K nonn

%O 1,12

%A _Ilya Gutkovskiy_, Aug 21 2021