OFFSET
1,2
COMMENTS
Except for the numbers 2, 9 and 10 this sequence is conjectured to be the same as A001013.
Every r! is a member for r>2, for (r!)! = (r!)*(r!-1)!. - Amarnath Murthy, Sep 11 2002
By Murthy's trick, if k>2 is a product of factorials then k is a term. So half of the above conjecture is true: A001013 is a subsequence except for the number 2. - Jonathan Sondow, Nov 08 2004
If there exists another term of this sequence not also in A001013, it must be >= 100000. - Charlie Neder, Oct 07 2018
An additional term of this sequence not in A001013 must be > 5000000. Can it be shown that no such terms exist using results on consecutive smooth numbers? - Charlie Neder, Jan 14 2019
REFERENCES
R. K. Guy, Unsolved Problems in Number Theory, B23.
LINKS
Charlie Neder, Table of n, a(n) for n = 1..222
Eric Weisstein's World of Mathematics, Factorial Products
EXAMPLE
1! = 0! (or, 1! is the empty product), 4! = 2!*2!*3!, 6! = 3!*5!, 8! = (2!)^3*7!, 9! = 2!*3!*3!*7!, 10! = 6!*7!, etc.
CROSSREFS
KEYWORD
easy,nonn,nice
AUTHOR
EXTENSIONS
More terms from Jud McCranie, Sep 13 2002
Edited by Dean Hickerson, Sep 17 2002
STATUS
approved