Factorion
A factorion is an integer which is equal to the sum of factorials of its digits. There are exactly four such numbers:
1 = 1!
(1)
2 = 2!
(2)
145 = 1!+4!+5!
(3)
40585 = 4!+0!+5!+8!+5!
(4)
(OEIS A014080; Gardner 1978, Madachy 1979, Pickover 1995). Obviously, the factorion of an n-digit number cannot exceed n·9!.
See also
Factorial, Factorial SumsExplore with Wolfram|Alpha
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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
FactorionCite this as:
Weisstein, Eric W. "Factorion." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Factorion.html