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 A127660 #17 Feb 17 2024 23:43:46
%S A127660 90972,100548,454860,502740,937692,968436,1000692,1106028,1182636,
%T A127660 1307124,1383732,1536416,1546524,1709316,2092356,2312604,2502528,
%U A127660 2638188,2690100,2820132,2915892,3116988,3365964,3720276,3729852,3907008,3911796,4122468,4248552,4275684
%N A127660 Integers whose exponential aliquot sequences end in an exponential amicable pair.
%C A127660 Sometimes called the exponential 2-cycle attractor set. The first 10 terms of this sequence are the same as the first 10 terms of A127659.
%H A127660 Amiram Eldar, <a href="/A127660/b127660.txt">Table of n, a(n) for n = 1..10000</a>
%H A127660 Peter Hagis, Jr., <a href="https://doi.org/10.1155/S0161171288000407">Some results concerning exponential divisors</a>, Internat. J. Math. & Math. Sci., Vol. 11, No. 2, (1988), pp. 343-350.
%H A127660 J. O. M. Pedersen, <a href="http://amicable.homepage.dk/tables.htm">Tables of Aliquot Cycles</a>. [Broken link]
%H A127660 J. O. M. Pedersen, <a href="http://web.archive.org/web/20140502102524/http://amicable.homepage.dk/tables.htm">Tables of Aliquot Cycles</a>. [Via Internet Archive Wayback-Machine]
%H A127660 J. O. M. Pedersen, <a href="/A063990/a063990.pdf">Tables of Aliquot Cycles</a>. [Cached copy, pdf file only]
%e A127660 a(11) = 1383732 because the eleventh integer whose exponential aliquot sequence ends in an exponential amicable pair is 1383732.
%t A127660 ExponentialDivisors[1]={1};ExponentialDivisors[n_]:=Module[{}, {pr,pows}=Transpose@FactorInteger[n];divpowers=Distribute[Divisors[pows],List];Sort[Times@@(pr^Transpose[divpowers])]];se[n_]:=Plus@@ExponentialDivisors[n]-n;g[n_] := If[n > 0, se[n], 0];eTrajectory[n_] := Most[NestWhileList[g, n, UnsameQ, All]];ExponentialAmicableNumberQ[k_]:=If[Nest[se,k,2]==k && !se[k]==k,True,False];Select[Range[5 10^6],ExponentialAmicableNumberQ[Last[eTrajectory[ # ]]] &]
%t A127660 f[p_, e_] := DivisorSum[e, p^# &]; s[0] = s[1] = 0; s[n_] := Times @@ f @@@ FactorInteger[n] - n; q[n_] := Module[{v = NestWhileList[s, n, UnsameQ, All]}, v[[-2]] != v[[-1]] > 0 && v[[-3]] == v[[-1]]]; Select[Range[10^6], q] (* _Amiram Eldar_, Mar 11 2023 *)
%Y A127660 Cf. A127656, A127657, A127658.
%Y A127660 Subsequences: A127659, A126165, A126166.
%K A127660 nonn
%O A127660 1,1
%A A127660 _Ant King_, Jan 25 2007