

A034878


Numbers n such that n! can be written as the product of smaller factorials.


16



1, 4, 6, 8, 9, 10, 12, 16, 24, 32, 36, 48, 64, 72, 96, 120, 128, 144, 192, 216, 240, 256, 288, 384, 432, 480, 512, 576, 720, 768, 864, 960, 1024, 1152, 1296, 1440, 1536, 1728, 1920, 2048, 2304, 2592, 2880, 3072, 3456, 3840, 4096, 4320, 4608, 5040, 5184
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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 n>2 is a product of factorials then n is a member. 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
Index entries for sequences related to factorial numbers


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

Cf. A075082, A001013.
Sequence in context: A275722 A047820 A248807 * A173328 A116661 A109104
Adjacent sequences: A034875 A034876 A034877 * A034879 A034880 A034881


KEYWORD

easy,nonn,nice


AUTHOR

Erich Friedman


EXTENSIONS

More terms from Jud McCranie, Sep 13 2002
Edited by Dean Hickerson, Sep 17 2002


STATUS

approved



