A065731 Largest square <= n!.

1, 1, 1, 4, 16, 100, 676, 4900, 40000, 362404, 3625216, 39904489, 478996996, 6226945921, 87177877081, 1307672296225, 20922784184449, 355687416544329, 6402373660047556, 121645099966283776, 2432902006216007824, 51090942169052381124, 1124000727752683686724

Offset: 0

Author

Labos Elemer, Nov 15 2001

Keywords

• easy
• nonn

Links

• Harry J. Smith, Table of n, a(n) for n = 0..100

Crossrefs

Cf. A048760, A000142, A065730-A065741.

Programs

Magma

[Floor(Sqrt(Factorial(n)))^2: n in [0..25]]; // Vincenzo Librandi, Dec 07 2018

Mathematica

Array[Floor@ Sqrt[#!]^2 &, 21, 0] (* Michael De Vlieger, Dec 06 2018 *)

PARI

a(n) = { sqrtint(n!)^2 } \\ Harry J. Smith, Oct 28 2009

Formula

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

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

Extensions

Offset changed from 1 to 0 by Harry J. Smith, Oct 28 2009