A333807 - OEIS

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

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OFFSET

1,12

LINKS

Table of n, a(n) for n=1..90.

FORMULA

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

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

CROSSREFS

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