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

2,1

Links

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

Example

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

Mathematica

s={2}; f1=4; f2=2; k=2; Do[f1=f1*n^2; While[f2<f1, k++; f2=f2*k]; AppendTo[s, k-1], {n, 3, 100}]; s (* Zak Seidov, May 08 2013 *)

Prog

(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

Crossrefs

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

Sequence in context: A226720 A047212 A358845 * A303589 A106829 A190228

Adjacent sequences: A121344 A121345 A121346 * A121348 A121349 A121350

Keyword

nonn

Author

Hugo Pfoertner, Aug 15 2006

Extensions

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

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

Status

approved