A114286 Sum of the cubes of the first n cubefree numbers.

0, 1, 9, 36, 100, 225, 441, 784, 1513, 2513, 3844, 5572, 7769, 10513, 13888, 18801, 24633, 31492, 39492, 48753, 59401, 71568, 87193, 104769, 126721, 151110, 178110, 207901, 243838, 283142, 326017, 372673, 423326, 478198, 537517, 606438, 680526

Offset

0,3

Links

Table of n, a(n) for n=0..36.

Eric Weisstein's World of Mathematics, Cubefree.

Formula

a(n) = Sum_{k=1..n} A004709(k)^3.

a(n) ~ c * n^4, where c = zeta(3)^3/4 = 0.4342252653... . - Amiram Eldar, Feb 20 2024

Example

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.

Mathematica

cubeFreeQ[n_] := Max[FactorInteger[n][[;; , 2]]] < 3; Join[{0}, Accumulate[Select[Range[50], cubeFreeQ]^3]] (* Amiram Eldar, Feb 20 2024 *)

Crossrefs

Cf. A004709, A114287.

Sequence in context: A231686 A231688 A000537 * A098928 A139469 A103158

Adjacent sequences: A114283 A114284 A114285 * A114287 A114288 A114289

Keyword

easy,nonn

Author

Jonathan Vos Post, Nov 20 2005

Status

approved