A114287 - OEIS

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A114287

Sum of the cubes of the first n noncubefree numbers.

0, 512, 4608, 18432, 38115, 70883, 134883, 245475, 402939, 578555, 840699, 1213947, 1725947, 2257388, 2938860, 3823596, 4948460, 6208172, 7613100, 9341100, 11294225, 13391377, 15851752, 18367208, 21353192, 24865000, 28961000

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..26.

FORMULA

a(n) = Sum_{k=1..n} A046099(k)^3.

a(n) ~ c * n^4, where c = (zeta(3)/(zeta(3)-1))^3/4 = 52.6373493984... . - Amiram Eldar, Feb 20 2024

EXAMPLE

a(10) = 8^3 + 16^3 + 24^3 + 27^3 + 32^3 + 40^3 + 48^3 + 54^3 + 56^3 + 64^3 = 840699.

MATHEMATICA

noncubeFreeQ[n_] := Max[FactorInteger[n][[;; , 2]]] > 2; Join[{0}, Accumulate[Select[Range[200], noncubeFreeQ]^3]] (* Amiram Eldar, Feb 20 2024 *)