

A109095


Numbers n such that n! is the product of exactly two smaller factorials.


10




OFFSET

1,1


COMMENTS

x! is considered to be a trivial solution because (x!)! can be written as x!*(x!1)!
All terms except 10 appear to be trivial solutions. Every factorial appears in this sequence.


REFERENCES

Richard K. Guy, Unsolved Problems in Number Theory, B23 Equal products of factorials, Springer, Third Edition, 2004, p. 123.
Laurent Habsieger (2019), Explicit bounds for the Diophantine equation A!B! = C!. Fibonacci Quarterly. 57, 1.


LINKS

Table of n, a(n) for n=1..7.
Laurent Habsieger, Explicit Bounds For The Diophantine Equation A!B! = C!, arXiv:1903.08370 [math.NT], 2019.


EXAMPLE

10! = 6! * 7!, so 10 is in the sequence.


CROSSREFS

Cf. A000142, A034878, A001013, A003135, A058295, A075082, A109096, A109097.
Sequence in context: A108899 A074289 A109099 * A323107 A077621 A298736
Adjacent sequences: A109092 A109093 A109094 * A109096 A109097 A109098


KEYWORD

nonn,more


AUTHOR

Jud McCranie, Jun 19 2005


EXTENSIONS

Definition corrected by Jon E. Schoenfield, Jul 02 2010


STATUS

approved



