

A254499


Amicable factorions.


4




OFFSET

1,2


COMMENTS

The members of a pair of numbers p and q are called amicable factorions if each is equal to the sum of the factorials of the base10 digits of the other. The only six pairs (p,q) are (1, 1), (2, 2), (145, 145), (871,45361), (872, 45362), (40585, 40585).
Peter Kiss (1977) showed there are no further terms.  N. J. A. Sloane, Mar 17 2019


REFERENCES

P. Kiss, A generalization of a problem in number theory, Math. Sem. Notes Kobe Univ., 5 (1977), no. 3, 313317. MR 0472667 (57 #12362).


LINKS

Table of n, a(n) for n=1..8.
S. S. Gupta, Sum of the factorials of the digits of integers, Math. Gaz. 88 (512) (2004) 258261
P. Kiss, A generalization of a problem in number theory, [Hungarian], Mat. Lapok, 25 (No. 12, 1974), 145149.
G. D. Poole, Integers and the sum of the factorials of their digits, Math. Mag., 44 (1971), 278279, [JSTOR].
H. J. J. te Riele, Iteration of numbertheoretic functions, Nieuw Archief v. Wiskunde, (4) 1 (1983), 345360. See Example I.1.b.
Eric Weisstein's World of Mathematics, Factorion


FORMULA

n such that f(f(n))=n, where f(k)=A061602(k).


EXAMPLE

871 and 45361 are in the sequence because:
871 => 8!+7!+1! = 40320 +5040 + 1 = 45361;
45361 => 4!+5!+3!+6!+1! = 24 + 120 + 6 + 720 + 1 = 871.


MATHEMATICA

Select[Range[10^6], Plus @@ (IntegerDigits[Plus @@ (IntegerDigits[ # ]!) ]!) == # &]


CROSSREFS

Cf. A061602, A306955.
A014080 and A214285 are subsets.
Sequence in context: A188284 A306955 A228507 * A071064 A265442 A014080
Adjacent sequences: A254496 A254497 A254498 * A254500 A254501 A254502


KEYWORD

nonn,fini,full,base


AUTHOR

Michel Lagneau, Jan 31 2015


STATUS

approved



