*N.B. A detailed on-line essay by S. Finch
was the starting point for this entry.*

Let be the number of ways in which the Factorial can be decomposed into Factors of
the form arranged in nondecreasing order. Also define

(1) |

(2) |

(3) |

so

(4) |

(5) |

(6) |

**References**

Alladi, K. and Grinstead, C. ``On the Decomposition of into Prime Powers.'' *J. Number Th.* **9**,
452-458, 1977.

Finch, S. ``Favorite Mathematical Constants.'' http://www.mathsoft.com/asolve/constant/aldgrns/aldgrns.html

Guy, R. K. ``Factorial as the Product of Large Factors.'' §B22 in
*Unsolved Problems in Number Theory, 2nd ed.* New York: Springer-Verlag, p. 79, 1994.

© 1996-9

1999-05-25