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 A127163 Integers whose aliquot sequences terminate by encountering the prime 3. Also known as the prime family 3. 4
 3, 4, 9, 12, 15, 16, 26, 30, 33, 42, 45, 46, 52, 54, 66, 72, 78, 86, 87, 90, 102, 105, 114, 121, 123, 126, 135, 144, 165, 166, 174, 186, 198, 207, 212, 243, 246, 247, 249, 258, 259, 270 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS This sequence is complete only as far as the last term given, for the eventual fate of the aliquot sequence generated by 276 is not (yet) known REFERENCES Benito, Manuel and Varona, Juan L.; Advances In Aliquot Sequences, Mathematics of Computation, Vol. 68, No. 225, (1999), pp. 389-393. Benito, Manuel; Creyaufmueller, Wolfgang; Varona, Juan Luis; and Zimmermann, Paul; Aliquot Sequence 3630 Ends After Reaching 100 Digits; Experimental Mathematics, Vol. 11, No. 2, Natick, MA, 2002, pp. 201-206. LINKS Wolfgang Creyaufmueller, Aliquot sequences. FORMULA Define s(i)=sigma(i)-i=A000203(i)-i. Then if the aliquot sequence obtained by repeatedly applying the mapping i->s(i) terminates by encountering the prime 3 as a member of its trajectory, i is included in this sequence EXAMPLE a(5)=15 because the fifth integer whose aliquot sequence terminates by encountering the prime 3 as a member of its trajectory is 15. The complete aliquot sequence generated by iterating the proper divisors of 15 is 15->9->4->3->1->0 MATHEMATICA s[n_] := DivisorSigma[1, n] - n; g[n_] := If[n > 0, s[n], 0]; Trajectory[n_] := Most[NestWhileList[g, n, UnsameQ, All]]; Select[Range[275], MemberQ[Trajectory[ # ], 3] &] CROSSREFS Cf. A080907, A127161, A127162, A127164, A098007, A121507, A098008, A007906, A063769, A115060, A115350. Sequence in context: A287450 A010394 A010427 * A058503 A112169 A155564 Adjacent sequences:  A127160 A127161 A127162 * A127164 A127165 A127166 KEYWORD hard,nonn AUTHOR Ant King, Jan 07 2007 STATUS approved

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Last modified November 18 09:13 EST 2017. Contains 294879 sequences.