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 A127658 #16 Mar 11 2023 08:05:36
%S A127658 900,1352,1728,2880,2916,3000,3750,4356,5292,6480,6760,8100,8640,9464,
%T A127658 9900,10404,10648,11700,12000,12096,13500,14580,14872,15300,15552,
%U A127658 15876,16000,16200,16224,17100,17836,18252,19008,19044,20160,20412,20700,21780,22464,22500
%N A127658 Exponential aspiring numbers.
%C A127658 Exponential aspiring numbers are those integers whose exponential aliquot sequences end in an e-perfect number, but that are not e-perfect numbers themselves.
%H A127658 Amiram Eldar, <a href="/A127658/b127658.txt">Table of n, a(n) for n = 1..10000</a>
%H A127658 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 A127658 J. O. M. Pedersen, <a href="http://amicable.homepage.dk/tables.htm">Tables of Aliquot Cycles</a>. [Broken link]
%H A127658 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 A127658 J. O. M. Pedersen, <a href="/A063990/a063990.pdf">Tables of Aliquot Cycles</a>. [Cached copy, pdf file only]
%e A127658 a(5) = 2916 because the fifth non-e-perfect number whose exponential aliquot sequence ends in an e-perfect number is 2916.
%t A127658 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]];Select[Range[25000],ExponentialPerfectNumberQ[Last[eTrajectory[ # ]]] && !ExponentialPerfectNumberQ[ # ]&]
%t A127658 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[[-1]] != n && v[[-2]] == v[[-1]] > 0]; Select[Range[32000], q] (* _Amiram Eldar_, Mar 11 2023 *)
%Y A127658 Cf. A127656, A127657, A127659, A127660, A054979.
%K A127658 nonn
%O A127658 1,1
%A A127658 _Ant King_, Jan 25 2007