A120721 Partial sums of A079645.

1, 3, 6, 10, 15, 21, 28, 36, 46, 58, 72, 88, 106, 126, 148, 172, 198, 225, 255, 288, 324, 363, 405, 450, 498, 549, 603, 660, 720, 783, 847, 915, 987, 1063, 1143, 1227, 1315, 1407, 1503, 1603, 1707, 1815, 1927, 2043, 2163, 2287, 2412, 2542, 2677, 2817, 2962, 3112, 3267

Offset: 1

Author

N. J. A. Sloane, Oct 29 2006

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A079645, A032378, A112873.

Programs

Magma

A079645:=[n: n in [1..500] | n mod Floor(n^(1/3)) eq 0 ];
[(&+[A079645[k]: k in [1..n]]): n in [1..100]]; // G. C. Greubel, Jul 20 2023

Mathematica

Accumulate[Select[Range[300],Divisible[#,Floor[CubeRoot[#]]]&]] (* Harvey P. Dale, Jun 19 2023 *)

SageMath

A079645=[j for j in (1..500) if j%(floor(j^(1/3)))==0]
def A120721(n): return sum(A079645[k] for k in range(n+1))
[A120721(n) for n in range(101)] # G. C. Greubel, Jul 20 2023

Formula

a(n) = Sum_{j=1..n} A079645(j).

a(n) ~ 2^(5/2)*n^(5/2)/(5*3^(3/2)) - 5*n^2/6. - Vaclav Kotesovec, Oct 13 2024