

A003135


n! is a nontrivial product of factorials. It is conjectured that the list is complete.


10




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

Table of n, a(n) for n=1..3.
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), 2544.
Index entries for sequences related to factorial numbers


EXAMPLE

9! = 2! * 3! * 3! * 7! and 7 < 91, so 9 is in the sequence.
10! = 6! * 7! or 10! = 3! * 5! * 7! and 7 < 101, so 10 is in the sequence.
16! = 2! * 5! * 14! and 14 < 161, 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

N. J. A. Sloane


STATUS

approved



