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%I #31 Apr 04 2015 10:02:00
%S 2,6,15,77,185,187,475,3820,4043,4090,11231,30589,57023,126815,131055,
%T 983032,983033,2617339,4046839,11534206,11534207,65011702,66777087,
%U 368279551,469745405,973061887,1064828671
%N Smallest integer m > 1 such that m!^(m + n) divides (m^2)!.
%C The constraint m > 1 is necessary because (1^2)! = 1.
%C The motivation for this sequence came from comments on the sequence A246048 by _M. F. Hasler_.
%C The integer (3820^2)!/(3820!)^3828 related to a(8) has 52166326 digits, so it isn't easy to find more terms.
%C a(28) > 1.5 * 10^9. - _Hiroaki Yamanouchi_, Sep 29 2014
%e a(4) = 77 because 77!^(77 + 4) divides (77^2)! and 77 is the smallest integer m, m > 1, with this property.
%o (PARI) for(n=1, 7, m=2; while((m^2)!%(m!^(m+n)), m++); print1(m", ")) \\ _Jens Kruse Andersen_, Aug 31 2014
%o (PARI) n=f=1; for(m=2, 5000, f*=m; s=m^2; forprime(p=2, m, e=0; b=p; while(b<=s, e+=s\b; b*=p); if(valuation(f,p)*(m+n)>e, next(2))); print1(m", "); n++) \\ Faster program. _Jens Kruse Andersen_, Aug 31 2014
%Y Cf. A096126, A096127, A246048.
%K nonn,more,hard
%O 1,1
%A _Farideh Firoozbakht_, Aug 24 2014
%E a(9)-a(13) from _Jens Kruse Andersen_, Aug 31 2014
%E a(14)-a(27) from _Hiroaki Yamanouchi_, Sep 29 2014
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