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

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

Links

Table of n, a(n) for n=1..80.

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

Cf. A001157, A050999, A333805, A333807, A339353, A347162.

Sequence in context: A010177 A096089 A010176 * A347173 A351647 A168644

Adjacent sequences: A347158 A347159 A347160 * A347162 A347163 A347164

Keyword

nonn

Author

Ilya Gutkovskiy, Aug 20 2021

Status

approved