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

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 *)

Crossrefs

Cf. A046099, A114286.

Sequence in context: A017067 A186845 A239917 * A061209 A017259 A017367

Adjacent sequences: A114284 A114285 A114286 * A114288 A114289 A114290

Keyword

easy,nonn

Author

Jonathan Vos Post, Nov 20 2005

Status

approved