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A254499
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Amicable factorions.
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5
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OFFSET
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1,2
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COMMENTS
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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
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REFERENCES
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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).
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LINKS
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Eric Weisstein's World of Mathematics, Factorion
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FORMULA
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n such that f(f(n))=n, where f(k)=A061602(k).
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EXAMPLE
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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.
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MATHEMATICA
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Select[Range[10^6], Plus @@ (IntegerDigits[Plus @@ (IntegerDigits[ # ]!) ]!) == # &]
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CROSSREFS
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KEYWORD
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nonn,fini,full,base
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AUTHOR
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STATUS
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approved
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