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A034876 Number of ways to write n! as a product of smaller factorials each greater than 1. 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; refs; listen; history; text; internal format)
OFFSET

1,10

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, Dec 15 2004

REFERENCES

R. K. Guy, Unsolved Problems in Number Theory, B23.

LINKS

Table of n, a(n) for n=1..105.

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.

Sequence in context: A219558 A279210 A232243 * A091393 A284557 A182032

Adjacent sequences:  A034873 A034874 A034875 * A034877 A034878 A034879

KEYWORD

easy,nonn,nice

AUTHOR

Erich Friedman

EXTENSIONS

Corrected by Jonathan Sondow, Dec 18 2004

STATUS

approved

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Last modified July 23 14:59 EDT 2017. Contains 289688 sequences.