The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A034878 Numbers n such that n! can be written as the product of smaller factorials. 18
 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 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 EXTENSIONS More terms from Jud McCranie, Sep 13 2002 Edited by Dean Hickerson, Sep 17 2002 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified April 18 04:49 EDT 2021. Contains 343072 sequences. (Running on oeis4.)