A358038 Partial sums of the cubefree numbers.

1, 3, 6, 10, 15, 21, 28, 37, 47, 58, 70, 83, 97, 112, 129, 147, 166, 186, 207, 229, 252, 277, 303, 331, 360, 390, 421, 454, 488, 523, 559, 596, 634, 673, 714, 756, 799, 843, 888, 934, 981, 1030, 1080, 1131, 1183, 1236, 1291, 1348, 1406, 1465, 1525, 1586, 1648, 1711

Offset: 1

Author

Amiram Eldar, Oct 29 2022

Keywords

• nonn

Comments

First differs from A025706 and A025730 at n = 14.

The analogous sequence with squarefree numbers is A173143.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Zhu Weiyi, On the cube free number sequences, Smarandache Notions J., Vol. 14 (2004), pp. 199-202.

Crossrefs

Cf. A002117, A004709, A173143.

Cf. A025706, A025730.

Programs

Mathematica

Accumulate[Select[Range[100], Max[FactorInteger[#][[;; , 2]]] < 3 &]]

Formula

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

a(n) = (zeta(3)/2)*n^2 + O(n^(3/2+eps)) (Weiyi, 2004).

Extensions

Corrected by Amiram Eldar, Jan 02 2024