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%I #17 Feb 20 2024 02:31:48
%S 0,1,9,36,100,225,441,784,1513,2513,3844,5572,7769,10513,13888,18801,
%T 24633,31492,39492,48753,59401,71568,87193,104769,126721,151110,
%U 178110,207901,243838,283142,326017,372673,423326,478198,537517,606438,680526
%N Sum of the cubes of the first n cubefree numbers.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Cubefree.html">Cubefree</a>.
%F a(n) = Sum_{k=1..n} A004709(k)^3.
%F a(n) ~ c * n^4, where c = zeta(3)^3/4 = 0.4342252653... . - _Amiram Eldar_, Feb 20 2024
%e 1^3 + 2^3 + 3^3 + 4^3 + 5^3 + 6^3 + 7^3 + 9^3 + 10^3 + 11^3 = 3844 = 2^2 * 31^2.
%t cubeFreeQ[n_] := Max[FactorInteger[n][[;; , 2]]] < 3; Join[{0}, Accumulate[Select[Range[50], cubeFreeQ]^3]] (* _Amiram Eldar_, Feb 20 2024 *)
%Y Cf. A004709, A114287.
%K easy,nonn
%O 0,3
%A _Jonathan Vos Post_, Nov 20 2005
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