A121347 Largest number whose factorial is less than (n!)^2.

2, 4, 5, 7, 9, 10, 12, 14, 15, 17, 19, 20, 22, 24, 26, 27, 29, 31, 32, 34, 36, 38, 39, 41, 43, 44, 46, 48, 50, 51, 53, 55, 57, 58, 60, 62, 64, 65, 67, 69, 71, 72, 74, 76, 78, 79, 81, 83, 85, 87, 88, 90, 92, 94, 95, 97, 99, 101, 102, 104, 106, 108, 110, 111, 113, 115, 117, 118

Offset: 2

Author

Hugo Pfoertner, Aug 15 2006

Keywords

• nonn

Examples

			a(3)=4 because 4!=24 is the largest factorial not exceeding (3!)^2=36.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 2..10000

Crossrefs

Cf. A121348 [difference between (n!)^2 and the next smaller factorial].

Programs

Mathematica

s={2};f1=4;f2=2;k=2;Do[f1=f1*n^2;While[f2Zak Seidov, May 08 2013 *)

PARI

A121347(n)= { local(lognf=2*sum(s=1,n,log(s)),k=1) ; while(1, if( sum(s=1,k,log(s))< lognf, k++, return(k-1) ; ) ; ) ; }
{ for(n=2,80, print1(A121347(n),", ") ; ) ; } \\ R. J. Mathar, May 12 2007

Extensions

a(2) corrected by Jon E. Schoenfield, Aug 27 2006

More terms from R. J. Mathar, May 12 2007