This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A127164 #9 Jun 07 2023 10:30:18 %S A127164 7,8,10,14,20,22,34,38,49,62,75,118,148,152,169,188,213,215 %N A127164 Integers whose aliquot sequences terminate by encountering the prime 7. Also known as the prime family 7. %C A127164 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. %D A127164 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 A127164 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 A127164 Wolfgang Creyaufmueller, <a href="http://www.aliquot.de/aliquote.htm">Aliquot sequences</a>. %F A127164 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. %e A127164 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 %t A127164 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] &] %Y A127164 Cf. A080907, A127161, A127162, A127163, A098007, A121507, A098008, A007906, A063769, A115060, A115350. %K A127164 hard,nonn %O A127164 1,1 %A A127164 _Ant King_, Jan 07 2007