id:A034876 - OEIS Search Results

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Number of ways to write n! as a product of smaller factorials each greater than 1.

+0
2

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 (list; graph; listen)

	OFFSET	`1,10`
	COMMENT	`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!)^pn! and n is prime. - Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Dec 15 2004`
	REFERENCES	`R. K. Guy, Unsolved Problems in Number Theory, B23.`
	LINKS	`Index entries for sequences related to factorial numbers.` `Eric Weisstein's World of Mathematics, Factorial Products`
	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.`
	CROSSREFS	`Cf. A034878, A001013, A075082.` `Adjacent sequences: A034873 A034874 A034875 this_sequence A034877 A034878 A034879` `Sequence in context: A069846 A070097 A096271 this_sequence A091393 A110270 A123635`
	KEYWORD	`easy,nonn,nice`
	AUTHOR	`Erich Friedman (erich.friedman(AT)stetson.edu)`
	EXTENSIONS	`Corrected by Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Dec 18 2004`

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Last modified October 15 09:18 EDT 2008. Contains 145015 sequences.

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