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A034876
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Number of ways to write n! as a product of smaller factorials each greater than 1.
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2
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0, 0, 0, 1, 0, 1, 0, 1, 1, 2, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0
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OFFSET
| 1,10
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COMMENTS
| By definition, a(n)>0 if and only if n is a member of A034878. If n>2, then a(n!)>max(a(n),a(n!-1)), as (n!)!=n!*(n!-1)!. Similarly, a(A001013(n))>0 for n>2. Clearly a(n)=0 if n is a prime A000040. So a(n+1)=1 if n=2^p-1 is a Mersenne prime A000668, as (n+1)!=(2!)^p*n! and n is prime. - Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Dec 15 2004
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REFERENCES
| R. K. Guy, Unsolved Problems in Number Theory, B23.
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LINKS
| Index entries for sequences related to factorial numbers.
Eric Weisstein's World of Mathematics, Factorial Products
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EXAMPLE
| a(10)=2 because 10!=3!*5!*7!=6!*7! are the only two ways to write 10! as a product of smaller factorials > 1.
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CROSSREFS
| Cf. A034878, A001013, A075082.
Sequence in context: A070097 A202523 A096271 * A091393 A110270 A187143
Adjacent sequences: A034873 A034874 A034875 * A034877 A034878 A034879
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KEYWORD
| easy,nonn,nice
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AUTHOR
| Erich Friedman (erich.friedman(AT)stetson.edu)
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EXTENSIONS
| Corrected by Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Dec 18 2004
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