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%I #23 Dec 17 2015 02:51:21
%S 9,10,16
%N n! is a nontrivial product of factorials. It is conjectured that the list is complete.
%C A "nontrivial" solution is one in which the largest x! in the product of a(n)! is such that x < a(n)-1. There are no other terms < 10^5. - _Jud McCranie_, Jun 15 2005
%D R. K. Guy, "Unsolved Problems in Number Theory", section B23.
%H P. Erdős, <a href="http://www.renyi.hu/~p_erdos/1976-39.pdf">Problems and results on number theoretic properties of consecutive integers and related questions</a>, Proc. 5th Manitoba Conf. Numerical Math., Congress. Num. 16 (1975), 25-44.
%H <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>
%e 9! = 2! * 3! * 3! * 7! and 7 < 9-1, so 9 is in the sequence.
%e 10! = 6! * 7! or 10! = 3! * 5! * 7! and 7 < 10-1, so 10 is in the sequence.
%e 16! = 2! * 5! * 14! and 14 < 16-1, so 16 is in the sequence.
%Y Cf. A034878, A001013, A058295, A075082, A109095, A109096, A109097, A109098.
%K nonn,bref,more,hard
%O 1,1
%A _N. J. A. Sloane_
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