A333807 Sum of odd divisors of n that are < sqrt(n).

0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 4, 1, 1, 4, 1, 1, 4, 1, 1, 4, 1, 1, 4, 1, 1, 9, 1, 1, 4, 1, 6, 4, 1, 1, 4, 6, 1, 4, 1, 1, 9, 1, 1, 4, 1, 6, 4, 1, 1, 4, 6, 8, 4, 1, 1, 9, 1, 1, 11, 1, 6, 4, 1, 1, 4, 13, 1, 4, 1, 1, 9, 1, 8, 4, 1, 6, 4, 1, 1, 11, 6, 1, 4, 1, 1, 18

Offset: 1

Author

Ilya Gutkovskiy, Apr 05 2020

Keywords

• nonn

Crossrefs

Cf. A000593, A069289, A070039, A333805, A333808, A333810.

Programs

Mathematica

Table[DivisorSum[n, # &, # < Sqrt[n] && OddQ[#] &], {n, 1, 90}]
nmax = 90; CoefficientList[Series[Sum[(2 k - 1) x^(2 k (2 k - 1))/(1 - x^(2 k - 1)), {k, 1, nmax}], {x, 0, nmax}], x] // Rest

Formula

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