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A347161
Sum of squares of odd divisors of n that are < sqrt(n).
3
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, 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, 1, 35, 1, 1, 59, 1, 26, 10, 1, 1, 10, 75, 1, 10, 1, 1, 35, 1, 50, 10, 1, 26
OFFSET
1,12
FORMULA
G.f.: Sum_{k>=1} (2*k - 1)^2 * x^(2*k*(2*k - 1)) / (1 - x^(2*k - 1)).
MATHEMATICA
Table[DivisorSum[n, #^2 &, # < Sqrt[n] && OddQ[#] &], {n, 1, 80}]
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
PROG
(PARI) a(n) = my(r=sqrt(n)); sumdiv(n, d, if ((d%2) && (d<r), d^2)); \\ Michel Marcus, Aug 21 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Aug 20 2021
STATUS
approved