A factorion is an Integer which is equal to the sum of Factorials of its digits. There are
exactly four such numbers:

(1) | |||

(2) | |||

(3) | |||

(4) |

(Sloane's A014080; Gardner 1978, Madachy 1979, Pickover 1995). The factorion of an -digit number cannot exceed digits.

**References**

Gardner, M. ``Factorial Oddities.'' Ch. 4 in
*Mathematical Magic Show: More Puzzles, Games, Diversions, Illusions and Other Mathematical Sleight-of-Mind from Scientific American.*
New York: Vintage, pp. 61 and 64, 1978.

Madachy, J. S. *Madachy's Mathematical Recreations.* New York: Dover, p. 167, 1979.

Pickover, C. A. ``The Loneliness of the Factorions.'' Ch. 22 in *Keys to Infinity.* New York:
W. H. Freeman, pp. 169-171 and 319-320, 1995.

© 1996-9

1999-05-26