login
Largest square <= n!.
3

%I #23 Dec 13 2024 12:38:46

%S 1,1,1,4,16,100,676,4900,40000,362404,3625216,39904489,478996996,

%T 6226945921,87177877081,1307672296225,20922784184449,355687416544329,

%U 6402373660047556,121645099966283776,2432902006216007824,51090942169052381124,1124000727752683686724

%N Largest square <= n!.

%H Harry J. Smith, <a href="/A065731/b065731.txt">Table of n, a(n) for n = 0..100</a>

%F a(n) = floor(sqrt(n!))^2.

%F a(n) = A048760(A000142(n)).

%t Array[Floor@ Sqrt[#!]^2 &, 21, 0] (* _Michael De Vlieger_, Dec 06 2018 *)

%o (PARI) a(n) = { sqrtint(n!)^2 } \\ _Harry J. Smith_, Oct 28 2009

%o (Magma) [Floor(Sqrt(Factorial(n)))^2: n in [0..25]]; // _Vincenzo Librandi_, Dec 07 2018

%Y Cf. A048760, A000142, A065730-A065741.

%K easy,nonn

%O 0,4

%A _Labos Elemer_, Nov 15 2001

%E Offset changed from 1 to 0 by _Harry J. Smith_, Oct 28 2009