A100196 Number of positive integer cubes <= n^2.
0, 1, 1, 2, 2, 2, 3, 3, 4, 4, 4, 4, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 17, 18, 18, 18
Offset: 0
Links
- Peter Munn, Table of n, a(n) for n = 0..10000
Programs
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Mathematica
Table[ Floor[n^(2/3)], {n, 0, 120}] (* Ray Chandler, Jan 09 2005 *) -
PARI
a(n)=floor(sqrtn(n^2,3)) \\ Charles R Greathouse IV, Mar 21 2012; corrected by Michel Marcus, Mar 08 2020
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PARI
a(n)=(n^2+.5)^(1/3)\1 \\ More careful rounding. - Charles R Greathouse IV, Mar 21 2012
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Python
from sympy import integer_nthroot def A100196(n): return integer_nthroot(n**2,3)[0] # Chai Wah Wu, Aug 15 2025
Formula
a(n) = floor(n^(2/3)). - Charles R Greathouse IV, Mar 21 2012
From Amiram Eldar, Apr 05 2025: (Start)
a(n) = A077113(n) - 1.
a(n) = A077106(n)^(1/3). (End)
Extensions
Corrected and extended by Ray Chandler, Jan 09 2005
a(0)=0 inserted by Sean A. Irvine, Jun 22 2020