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