

A014080


Factorions: equal to the sum of the factorials of their digits in base 10.


20




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,changed


AUTHOR

David W. Wilson


EXTENSIONS

Additional reference from Felice Russo.


STATUS

approved



