A003135 n! is a nontrivial product of factorials. It is conjectured that the list is complete.

9, 10, 16

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. Erdős, 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.

Index entries for sequences related to factorial numbers

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

N. J. A. Sloane

Status

approved