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 A254499 Amicable factorions. 5
 1, 2, 145, 871, 872, 40585, 45361, 45362 (list; graph; refs; listen; history; text; internal format)
 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 base-10 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, 313-317. 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) 258-261 P. Kiss, A generalization of a problem in number theory, [Hungarian], Mat. Lapok, 25 (No. 1-2, 1974), 145-149. G. D. Poole, Integers and the sum of the factorials of their digits, Math. Mag., 44 (1971), 278-279, [JSTOR]. H. J. J. te Riele, Iteration of number-theoretic functions, Nieuw Archief v. Wiskunde, (4) 1 (1983), 345-360. 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

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