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%I #11 Jan 07 2022 15:37:59
%S 0,1,1,1,1,1,1,1,1,1,1,28,1,1,28,1,1,28,1,1,28,1,1,28,1,1,28,1,1,153,
%T 1,1,28,1,126,28,1,1,28,126,1,28,1,1,153,1,1,28,1,126,28,1,1,28,126,
%U 344,28,1,1,153,1,1,371,1,126,28,1,1,28,469,1,28,1,1,153
%N Sum of cubes of odd divisors of n that are < sqrt(n).
%H Harvey P. Dale, <a href="/A347162/b347162.txt">Table of n, a(n) for n = 1..1000</a>
%F G.f.: Sum_{k>=1} (2*k - 1)^3 * x^(2*k*(2*k - 1)) / (1 - x^(2*k - 1)).
%t Table[DivisorSum[n, #^3 &, # < Sqrt[n] && OddQ[#] &], {n, 1, 75}]
%t nmax = 75; CoefficientList[Series[Sum[(2 k - 1)^3 x^(2 k (2 k - 1))/(1 - x^(2 k - 1)), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
%t scod[n_]:=Total[Select[Divisors[n],#<Sqrt[n]&&OddQ[#]&]^3]; Array[scod,80] (* _Harvey P. Dale_, Jan 07 2022 *)
%o (PARI) a(n) = my(r=sqrt(n)); sumdiv(n, d, if ((d%2) && (d<r), d^3)); \\ _Michel Marcus_, Aug 21 2021
%Y Cf. A001158, A051000, A333805, A333807, A339354, A347161.
%K nonn
%O 1,12
%A _Ilya Gutkovskiy_, Aug 20 2021
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