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.

A065733 Largest square <= n^3.

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%I A065733 #37 Dec 13 2024 12:38:43
%S A065733 0,1,4,25,64,121,196,324,484,729,961,1296,1681,2116,2704,3364,4096,
%T A065733 4900,5776,6724,7921,9216,10609,12100,13689,15625,17424,19600,21904,
%U A065733 24336,26896,29584,32761,35721,39204,42849,46656,50625,54756,59049,63504
%N A065733 Largest square <= n^3.
%H A065733 Harry J. Smith, <a href="/A065733/b065733.txt">Table of n, a(n) for n = 0..1000</a>
%F A065733 a(n) + A077116(n) = n^3.
%F A065733 a(n) = A048760(n^3).
%F A065733 n^3 - 2*n^(3/2) <= a(n) <= n^3. - _Charles R Greathouse IV_, Dec 05 2022
%F A065733 a(n) = A000093(n)^2. - _Amiram Eldar_, Jul 14 2024
%e A065733 a(10) = 961, as 961 = 31^2 is the largest square <= 1000 = 10^3.
%t A065733 Table[Floor[Sqrt[w^3]//N]^2, {w, 1, 50}]
%o A065733 (PARI) A065733(n)=sqrtint(n^3)^2  \\ _M. F. Hasler_, Oct 05 2013
%o A065733 (Haskell) a065733 n = head [x | x <- reverse [0.. n^3], a010052 x == 1] -- _Reinhard Zumkeller_, Oct 10 2013
%Y A065733 Cf. A000093, A048760, A065730-A065741, A087285.
%Y A065733 Cf. A077115, A077116, A077118, A077121.
%K A065733 easy,nonn
%O A065733 0,3
%A A065733 _Labos Elemer_, Nov 15 2001