A127163 Integers whose aliquot sequences terminate by encountering the prime 3. Also known as the prime family 3.

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

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; 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

Table of n, a(n) for n=1..42.

Manuel Benito and Juan L. Varona, Advances In Aliquot Sequences, Mathematics of Computation, Vol. 68, No. 225, (1999), pp. 389-393.

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