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 A014080 Factorions: equal to the sum of the factorials of their digits in base 10. 20
 1, 2, 145, 40585 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Base 6 also has four factorions, as does base 15. - Alonso del Arte, Oct 20 2012 This is row 10 of the table A193163. - M. F. Hasler, Nov 25 2015 REFERENCES J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 145, p. 50, Ellipses, Paris 2008. Clifford A. Pickover, A Passion for Mathematics, Wiley, 2005; see pp. 68, 305. Joe Roberts, "The Lure of the Integers", page 35. D. Wells, Curious and interesting numbers, Penguin Books, p. 125. LINKS Project Euler, Problem 34 Eric Weisstein's World of Mathematics, Factorion FORMULA If n has digits (d1,d2,...,dk) base 10, then n is on this list if and only if n = d1! + d2! + ... + dk!. EXAMPLE 1! + 4! + 5! = 1 + 24 + 120 = 145, therefore 145 is in the sequence. MATHEMATICA Select[Range[50000], Plus @@ (IntegerDigits[ # ]!) == # &] (* Alonso del Arte, Jan 14 2008 *) PROG (J) (#~ (= +/@:!@:("."0)@":"0)) i.1e5 NB. Stephen Makdisi, May 14 2016 CROSSREFS Cf. A193163. Sequence in context: A254499 A071064 A265442 * A182478 A214910 A251863 Adjacent sequences:  A014077 A014078 A014079 * A014081 A014082 A014083 KEYWORD nonn,fini,full,base AUTHOR EXTENSIONS Additional reference from Felice Russo. STATUS approved

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