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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

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

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Last modified September 18 11:42 EDT 2018. Contains 315130 sequences. (Running on oeis4.)