A077121 Number of integer squares <= n^3.

1, 2, 3, 6, 9, 12, 15, 19, 23, 28, 32, 37, 42, 47, 53, 59, 65, 71, 77, 83, 90, 97, 104, 111, 118, 126, 133, 141, 149, 157, 165, 173, 182, 190, 199, 208, 217, 226, 235, 244, 253, 263, 273, 282, 292, 302, 312, 323, 333, 344, 354, 365, 375, 386, 397, 408, 420

Offset: 0

Author

Reinhard Zumkeller, Oct 29 2002

Keywords

• nonn
• easy

Comments

a(n) = number of terms in n-th row of A167222. - Reinhard Zumkeller, Oct 31 2009

Examples

			Squares <= 3^3 = 27: 0, 1, 4, 9, 16 and 25, hence a(3) = 6.
		

Links

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

Crossrefs

Cf. A000093, A065733, A077113, A167222, A167223.

Programs

Mathematica

a[n_] := Floor[Sqrt[n^3]] + 1; Array[a, 100, 0] (* Amiram Eldar, Apr 06 2025 *)

Python

from math import isqrt
def A077121(n): return isqrt(n**3)+1 # Chai Wah Wu, Sep 08 2024

Formula

a(n) = floor(n^(3/2))+1 = A000093(n) + 1.