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Factorion

A factorion is a natural number that equals the sum of the factorials of its decimal digits. For example, 145 is a factorion because 1! + 4! + 5! = 1 + 24 + 120 = 145.

There are just four factorions (in base 10) and they are 1, 2, 145 and 40585 . "Factorion" is a name coined by book author Clifford A. Pickover in Chapter 22 of his book Keys to Infinity in a chapter titled "The Loneliness of the Factorions".