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 A003135 n! is a nontrivial product of factorials. It is conjectured that the list is complete. 10
 9, 10, 16 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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 REFERENCES R. K. Guy, "Unsolved Problems in Number Theory", section B23. LINKS P. ErdÅ‘s, Problems and results on number theoretic properties of consecutive integers and related questions, Proc. 5th Manitoba Conf. Numerical Math., Congress. Num. 16 (1975), 25-44. EXAMPLE 9! = 2! * 3! * 3! * 7! and 7 < 9-1, so 9 is in the sequence. 10! = 6! * 7! or 10! = 3! * 5! * 7! and 7 < 10-1, so 10 is in the sequence. 16! = 2! * 5! * 14! and 14 < 16-1, so 16 is in the sequence. CROSSREFS Cf. A034878, A001013, A058295, A075082, A109095, A109096, A109097, A109098. Sequence in context: A197113 A099616 A073829 * A105742 A105834 A280846 Adjacent sequences:  A003132 A003133 A003134 * A003136 A003137 A003138 KEYWORD nonn,bref,more,hard AUTHOR STATUS approved

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Last modified October 23 07:11 EDT 2019. Contains 328336 sequences. (Running on oeis4.)