Factorion

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)

(OEIS A014080; Gardner 1978, Madachy 1979, Pickover 1995). Obviously, the factorion of an -digit number cannot exceed .

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.

Sloane, N. J. A. Sequence A014080 in "The On-Line Encyclopedia of Integer Sequences."