A077113 Number of nonnegative integer cubes <= n^2.

1, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5, 5, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 17, 17, 18, 18, 18, 18, 18, 18, 19

Offset: 0

Author

Reinhard Zumkeller, Oct 29 2002

Keywords

• nonn
• easy

Comments

a(n) is the least number m such that m^3 > n^2. - Zak Seidov, May 03 2005

Examples

			Cubes <= 10^2: 0, 1, 8, 27 and 64, hence a(10) = 5.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A026409, A026414, A054071, A077106, A077121, A100196.

Programs

Mathematica

Table[Floor[n^(2/3) + 1], {n, 0, 100}] (* Zak Seidov, May 03 2005 *)

Python

from sympy import integer_nthroot
def A077113(n): return integer_nthroot(n**2,3)[0]+1 # Chai Wah Wu, Aug 15 2025

Formula

a(n) = floor(n^(2/3))+1.

a(n) = [x^(n^2)] (1/(1 - x))*Sum_{k>=0} x^(k^3). - Ilya Gutkovskiy, Apr 20 2018

a(n) = A100196(n) + 1. - Amiram Eldar, Apr 05 2025

Extensions

Edited by N. J. A. Sloane, Aug 29 2008 at the suggestion of R. J. Mathar