%I #19 Feb 20 2024 02:32:03

%S 0,512,4608,18432,38115,70883,134883,245475,402939,578555,840699,

%T 1213947,1725947,2257388,2938860,3823596,4948460,6208172,7613100,

%U 9341100,11294225,13391377,15851752,18367208,21353192,24865000,28961000

%N Sum of the cubes of the first n noncubefree numbers.

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

%F a(n) ~ c * n^4, where c = (zeta(3)/(zeta(3)-1))^3/4 = 52.6373493984... . - _Amiram Eldar_, Feb 20 2024

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

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

%Y Cf. A046099, A114286.

%K easy,nonn

%O 0,2

%A _Jonathan Vos Post_, Nov 20 2005