

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
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OFFSET

2,1


LINKS

Table of n, a(n) for n=2..69.


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, k1], {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(k1) ; ) ; ) ; } { 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: A286989 A226720 A047212 * 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



