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A121347
Largest number whose factorial is less than (n!)^2.
4
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
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
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