%I #21 Mar 30 2012 18:39:49
%S 1,0,0,6,24,12,10,20,16,28,25,22,33,30,28,28,39,35,36,44,44,42,44,50,
%T 50,50,57,57,56,58,65,64,64,72,72,70,75,80,80,78,80,88,88,86,88,95,95,
%U 94,96,102,104,102,104,111,111,110,112,120,119,118,120,122,125
%N a(n) = minimum value of the largest element of a nonempty set of positive integers > n such that their product is equal to n!, or 0 if no such set exists.
%C For n > 4, there is always the factorization n! = (2*n) * (n!/(2*n)), so a(n) is only 0 for n = 1 or 2. - Franklin T. Adams-Watters, Jul 28 2011.
%C It appears that this sequence is O(n). - Franklin T. Adams-Watters, Jul 28 2011.
%H William Rex Marshall, <a href="/A193429/a193429.txt">Pascal program</a>
%e For n=5, n! = 120. Any factorization of 120 into 3 (or more) factors will have a factor <= 5, so we take the most central factorization into two factors, 120 = 10*12, the maximum of {10, 12} is 12, thus a(5) = 12.
%Y Cf. A000142, A157017.
%K nonn
%O 0,4
%A _William Rex Marshall_, Jul 28 2011
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