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Search: id:A034878
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| A034878 |
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Numbers n such that n! can be written as the product of smaller factorials. |
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+0
15
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| 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; listen)
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OFFSET
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1,2
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COMMENT
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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 (amarnath_murthy(AT)yahoo.com), 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 (jsondow(AT)alumni.princeton.edu), Nov 08 2004
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REFERENCES
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R. K. Guy, Unsolved Problems in Number Theory, B23.
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LINKS
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Eric Weisstein's World of Mathematics, Factorial Products
Index entries for sequences related to factorial numbers
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EXAMPLE
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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.
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CROSSREFS
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Cf. A075082, A001013.
Sequence in context: A067013 A071070 A047820 this_sequence A116661 A109104 A073303
Adjacent sequences: A034875 A034876 A034877 this_sequence A034879 A034880 A034881
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KEYWORD
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easy,nonn,nice
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AUTHOR
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Erich Friedman (erich.friedman(AT)stetson.edu)
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EXTENSIONS
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More terms from Jud McCranie (JudMcCr(AT)BellSouth.net), Sep 13 2002
Edited by Dean Hickerson (dean(AT)math.ucdavis.edu), Sep 17 2002
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