A347172 - OEIS

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A347172

Sum of 4th powers of odd divisors of n that are < sqrt(n).

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

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OFFSET

1,12

LINKS

Table of n, a(n) for n=1..75.

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

CROSSREFS

Cf. A001159, A051001, A333805, A333807, A347142, A347161, A347162.