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A347162
Sum of cubes of odd divisors of n that are < sqrt(n).
4
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, 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, 344, 28, 1, 1, 153, 1, 1, 371, 1, 126, 28, 1, 1, 28, 469, 1, 28, 1, 1, 153
OFFSET
1,12
LINKS
FORMULA
G.f.: Sum_{k>=1} (2*k - 1)^3 * x^(2*k*(2*k - 1)) / (1 - x^(2*k - 1)).
MATHEMATICA
Table[DivisorSum[n, #^3 &, # < Sqrt[n] && OddQ[#] &], {n, 1, 75}]
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
scod[n_]:=Total[Select[Divisors[n], #<Sqrt[n]&&OddQ[#]&]^3]; Array[scod, 80] (* Harvey P. Dale, Jan 07 2022 *)
PROG
(PARI) a(n) = my(r=sqrt(n)); sumdiv(n, d, if ((d%2) && (d<r), d^3)); \\ Michel Marcus, Aug 21 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Aug 20 2021
STATUS
approved