

A127164


Integers whose aliquot sequences terminate by encountering the prime 7. Also known as the prime family 7.


4



7, 8, 10, 14, 20, 22, 34, 38, 49, 62, 75, 118, 148, 152, 169, 188, 213, 215
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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. 389393.
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. 201206.


LINKS

Table of n, a(n) for n=1..18.
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 7 as a member of its trajectory, i is included in this sequence.


EXAMPLE

a(5)=20 because the fifth integer whose aliquot sequence terminates by encountering the prime 7 as a member of its trajectory is 20. The complete aliquot sequence generated by iterating the proper divisors of 15 is 20>22>14>10>8>7>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[ # ], 7] &]


CROSSREFS

Cf. A080907, A127161, A127162, A127163, A098007, A121507, A098008, A007906, A063769, A115060, A115350.
Sequence in context: A243078 A048588 A141676 * A153972 A286420 A111064
Adjacent sequences: A127161 A127162 A127163 * A127165 A127166 A127167


KEYWORD

hard,nonn


AUTHOR

Ant King, Jan 07 2007


STATUS

approved



