A factorion is an integer which is equal to the sum of factorials of its digits. There are exactly four such
numbers:
(OEIS A014080; Gardner 1978, Madachy 1979, Pickover 1995). Obviously, the factorion of an 
-digit number cannot exceed 
.
See also
Factorial,
Factorial
Sums
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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."Referenced
on Wolfram|Alpha
Factorion
Cite this as:
Weisstein, Eric W. "Factorion." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Factorion.html
Subject classifications
