cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A100196 Number of positive integer cubes <= n^2.

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%I A100196 #32 Aug 15 2025 14:10:02
%S A100196 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,
%T A100196 10,10,10,10,11,11,11,11,11,12,12,12,12,12,13,13,13,13,13,13,14,14,14,
%U A100196 14,14,14,15,15,15,15,15,16,16,16,16,16,16,16,17,17,17,17,17,17,18,18,18
%N A100196 Number of positive integer cubes <= n^2.
%H A100196 Peter Munn, <a href="/A100196/b100196.txt">Table of n, a(n) for n = 0..10000</a>
%F A100196 a(n) = floor(n^(2/3)). - _Charles R Greathouse IV_, Mar 21 2012
%F A100196 From _Amiram Eldar_, Apr 05 2025:  (Start)
%F A100196 a(n) = A077113(n) - 1.
%F A100196 a(n) = A077106(n)^(1/3). (End)
%t A100196 Table[ Floor[n^(2/3)], {n, 0, 120}] (* _Ray Chandler_, Jan 09 2005 *)
%o A100196 (PARI) a(n)=floor(sqrtn(n^2,3)) \\ _Charles R Greathouse IV_, Mar 21 2012; corrected by _Michel Marcus_, Mar 08 2020
%o A100196 (PARI) a(n)=(n^2+.5)^(1/3)\1 \\ More careful rounding. - _Charles R Greathouse IV_, Mar 21 2012
%o A100196 (Python)
%o A100196 from sympy import integer_nthroot
%o A100196 def A100196(n): return integer_nthroot(n**2,3)[0] # _Chai Wah Wu_, Aug 15 2025
%Y A100196 Cf. A000196, A054846, A062108, A077106, A077113, A100197.
%K A100196 easy,nonn
%O A100196 0,4
%A A100196 _Giovanni Teofilatto_, Dec 27 2004
%E A100196 Corrected and extended by _Ray Chandler_, Jan 09 2005
%E A100196 a(0)=0 inserted by _Sean A. Irvine_, Jun 22 2020