A347162 Sum of cubes of odd divisors of n that are < sqrt(n).

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

Harvey P. Dale, Table of n, a(n) for n = 1..1000

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

Cf. A001158, A051000, A333805, A333807, A339354, A347161.

Sequence in context: A040786 A040785 A040784 * A347174 A352031 A174188

Adjacent sequences: A347159 A347160 A347161 * A347163 A347164 A347165

Keyword

nonn

Author

Ilya Gutkovskiy, Aug 20 2021

Status

approved