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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 17 08:54 EDT 2019. Contains 327127 sequences. (Running on oeis4.)