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%I #10 Jun 20 2018 01:29:36
%S 1,1,2,2,3,4,4,5,5,6,7,7,8,8,9,10,10,11,11,12,13,13,14,14,15,15,16,17,
%T 17,18,18,19,20,20,21,21,22,22,23,24,24,25,25,26,27,27,28,28,29,29,30,
%U 31,31,32,32,33,33,34,35,35,36,36,37,37,38,39,39,40,40,41,41,42,43,43
%N a(n) = Max { k | k! <= n! / k! } where m! = A000142(m), factorial.
%C Also a(n) is a largest m such that m! <= sqrt(n!). - _Zak Seidov_, Jul 07 2009
%H Harry J. Smith, <a href="/A064542/b064542.txt">Table of n, a(n) for n = 1..1000</a>
%e n = 12: 5040 = 1*2*3*4*5*6*7 <= 8*9*10*11*12 = 95040 and as 40320 = 1*2*3*4*5*6*7*8 > 9*10*11*12 = 11880 we have a(12) = 7.
%o (PARI) { m=2; for (n=1, 1000, s=sqrt(n!); while (m! <= s, m++); write("b064542.txt", n, " ", m - 1) ) } \\ _Harry J. Smith_, Sep 18 2009
%Y Cf. A000142, A060048.
%K nonn
%O 1,3
%A _Reinhard Zumkeller_, Oct 08 2001
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