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A127161 Integers whose aliquot sequences terminate by encountering a prime number.

%I A127161 #7 Jun 07 2023 11:02:53
%S A127161 2,3,4,5,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,26,27,29,
%T A127161 30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,
%U A127161 53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75
%N A127161 Integers whose aliquot sequences terminate by encountering a prime number.
%C A127161 This sequence is the same as A080907 from A080907's second term onwards.
%D A127161 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.
%H A127161 Manuel Benito and Juan L. Varona, <a href="https://doi.org/10.1090/S0025-5718-99-00991-6">Advances In Aliquot Sequences</a>, Mathematics of Computation, Vol. 68, No. 225, (1999), pp. 389-393.
%H A127161 Wolfgang Creyaufmueller, <a href="http://www.aliquot.de/aliquote.htm">Aliquot sequences</a>.
%F A127161 Define s(i)=sigma(i)-i=A000203(i)-i. Then if the aliquot sequence obtained by repeatedly iterating s contains a prime as a member of its trajectory, i is included in this sequence
%e A127161 a(10)=12 because the tenth integer whose aliquot sequence terminates by encountering a prime as a member of its trajectory is 12. The complete aliquot sequence generated by iterating the proper divisors of 12 is 12->16->15->9->4->3->1->0
%t A127161 s[n_] := DivisorSigma[1, n] - n; g[n_] := If[n > 0, s[n], 0]; Trajectory[n_] := Most[NestWhileList[g, n, UnsameQ, All]]; Select[Range[2, 275], Last[Trajectory[ # ]] == 0 &]
%Y A127161 Cf. A080907, A127162, A127163, A127164, A098007, A121507, A098008, A007906, A063769, A115060, A115350.
%K A127161 nonn
%O A127161 1,1
%A A127161 _Ant King_, Jan 06 2007