

A254499


Amicable factorions.


5




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

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



KEYWORD

nonn,fini,full,base


AUTHOR



STATUS

approved



