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A109095 Numbers n such that n! is the product of exactly two smaller factorials. 10
6, 10, 24, 120, 720, 5040, 40320 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 20 02:10 EDT 2019. Contains 328244 sequences. (Running on oeis4.)