login
A347172
Sum of 4th powers of odd divisors of n that are < sqrt(n).
1
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, 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, 2402, 82, 1, 1, 707, 1, 1, 2483, 1, 626, 82, 1, 1, 82, 3027, 1, 82, 1, 1, 707
OFFSET
1,12
FORMULA
G.f.: Sum_{k>=1} (2*k - 1)^4 * x^(2*k*(2*k - 1)) / (1 - x^(2*k - 1)).
MATHEMATICA
Table[DivisorSum[n, #^4 &, # < Sqrt[n] && OddQ[#] &], {n, 1, 75}]
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
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Aug 21 2021
STATUS
approved