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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

Table of n, a(n) for n=1..4.

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

David W. Wilson

EXTENSIONS

Additional reference from Felice Russo.

STATUS

approved

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Last modified December 5 19:19 EST 2016. Contains 278770 sequences.