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%I #18 Feb 26 2019 14:33:50
%S 3,4,7,6,17,8,21,20,24,12,70,14,32,55,63,18,80,20,99,73,48,24,191,78,
%T 56,121,130,30,224,32,204,108,72,203,323,38,80,126,398,42,293,44,193,
%U 505,96,48,575,200,312,162,225,54,485,302,522,180,120,60,898,62,128,660,682
%N Greatest k such that n^k divides (n^2)!.
%C If p is prime, a(p) = p+1, a(p^2) = floor((p^3 + p^2 + p + 1)/2).
%D Thread "100!" in rec.puzzles newsgroup, April 2007
%H Robert Israel, <a href="/A117134/b117134.txt">Table of n, a(n) for n = 2..10000</a> (n=2..103 from Vincenzo Librandi)
%e a(3)=4 because (3^2)! = 362880 = 3^4 * 4480 and 4480 is not divisible by 3.
%p seq(ordp((n^2)!,n), n=2..50);
%p # Alternative:
%p f:= proc(n) local F,m,t,v,j;
%p F:= ifactors(n)[2];
%p m:= infinity;
%p for t in F do
%p v:= add(floor(n^2/t[1]^j),j=1..ceil(log[t[1]](n^2)));
%p m:= min(m,floor(v/t[2]));
%p od;
%p m
%p end proc:
%p map(f, [$2..100]); # _Robert Israel_, Feb 26 2019
%t gkn[n_]:=Module[{c=(n^2)!,k},k=Floor[Log[c]/Log[n]]; While[!Divisible[ c,n^k], k--];k]; Array[gkn,70,2] (* _Harvey P. Dale_, Sep 14 2012 *)
%Y Cf. A011776.
%K nonn,look
%O 2,1
%A _Robert Israel_, Apr 26 2007
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