Calculus and Analysis > Special Functions > Factorials >
Number Theory > Special Numbers > Digit-Related Numbers >

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!.

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