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%I #18 Dec 19 2019 02:31:00
%S 2,4,5,7,9,10,12,14,15,17,19,20,22,24,26,27,29,31,32,34,36,38,39,41,
%T 43,44,46,48,50,51,53,55,57,58,60,62,64,65,67,69,71,72,74,76,78,79,81,
%U 83,85,87,88,90,92,94,95,97,99,101,102,104,106,108,110,111,113,115,117,118
%N Largest number whose factorial is less than (n!)^2.
%H Chai Wah Wu, <a href="/A121347/b121347.txt">Table of n, a(n) for n = 2..10000</a>
%e a(3)=4 because 4!=24 is the largest factorial not exceeding (3!)^2=36.
%t 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 *)
%o (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) ; ) ; ) ; }
%o { for(n=2,80, print1(A121347(n),", ") ; ) ; } \\ _R. J. Mathar_, May 12 2007
%Y Cf. A121348 [difference between (n!)^2 and the next smaller factorial].
%K nonn
%O 2,1
%A _Hugo Pfoertner_, Aug 15 2006
%E a(2) corrected by _Jon E. Schoenfield_, Aug 27 2006
%E More terms from _R. J. Mathar_, May 12 2007
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