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Search: id:A127163
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| A127163 |
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Integers whose aliquot sequences terminate by encountering the prime 3. Also known as the prime family 3. |
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+0
5
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| 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; listen)
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OFFSET
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1,1
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COMMENT
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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
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REFERENCES
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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; Zimmermann. Paul; Aliquot Sequence 3630 Ends After Reaching 100 Digits; Experimental Mathematics, Vol. 11, No. 2, Natick, MA, 2002, pp. 201-206.
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LINKS
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Wolfgang Creyaufmueller, Aliquot sequences.
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FORMULA
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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
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EXAMPLE
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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
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MATHEMATICA
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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] &]
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CROSSREFS
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Cf. A080907, A127161, A127162, A127164, A098007, A121507, A098008, A007906, A063769, A115060, A115350.
Sequence in context: A067163 A010394 A010427 this_sequence A058503 A112169 A105137
Adjacent sequences: A127160 A127161 A127162 this_sequence A127164 A127165 A127166
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KEYWORD
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hard,nonn
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AUTHOR
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Ant King (mathstutoring(AT)ntlworld.com), Jan 07 2007
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