A065733 Largest square <= n^3.
0, 1, 4, 25, 64, 121, 196, 324, 484, 729, 961, 1296, 1681, 2116, 2704, 3364, 4096, 4900, 5776, 6724, 7921, 9216, 10609, 12100, 13689, 15625, 17424, 19600, 21904, 24336, 26896, 29584, 32761, 35721, 39204, 42849, 46656, 50625, 54756, 59049, 63504
Offset: 0
Examples
a(10) = 961, as 961 = 31^2 is the largest square <= 1000 = 10^3.
Links
- Harry J. Smith, Table of n, a(n) for n = 0..1000
Programs
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Haskell
a065733 n = head [x | x <- reverse [0.. n^3], a010052 x == 1] -- Reinhard Zumkeller, Oct 10 2013
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Mathematica
Table[Floor[Sqrt[w^3]//N]^2, {w, 1, 50}] -
PARI
A065733(n)=sqrtint(n^3)^2 \\ M. F. Hasler, Oct 05 2013
Formula
a(n) + A077116(n) = n^3.
a(n) = A048760(n^3).
n^3 - 2*n^(3/2) <= a(n) <= n^3. - Charles R Greathouse IV, Dec 05 2022
a(n) = A000093(n)^2. - Amiram Eldar, Jul 14 2024