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 A127660 Integers whose exponential aliquot sequences end in an exponential amicable pair. 4
 90972, 100548, 454860, 502740, 937692, 968436, 1000692, 1106028, 1182636, 1307124, 1383732, 1536416, 1546524, 1709316, 2092356, 2312604, 2502528, 2638188, 2690100, 2820132, 2915892, 3116988, 3365964, 3720276, 3729852 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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 REFERENCES Hagis, Peter Jr.; Some Results Concerning Exponential Divisors, Internat. J. Math. & Math. Sci., Vol. 11, No. 2, (1988), pp. 343-350. LINKS J. O. M. Pedersen, Tables of Aliquot Cycles [Broken link] J. O. M. Pedersen, Tables of Aliquot Cycles [Via Internet Archive Wayback-Machine] J. O. M. Pedersen, Tables of Aliquot Cycles [Cached copy, pdf file only] EXAMPLE a(11)=1383732 because the eleventh integer whose exponential aliquot sequence ends in an exponential amicable pair is 1383732. MATHEMATICA 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[ # ]]] &] CROSSREFS Cf. A127656, A127657, A127658, A127659, A126165, A126166. Sequence in context: A183677 A015316 A212853 * A127659 A126165 A323753 Adjacent sequences:  A127657 A127658 A127659 * A127661 A127662 A127663 KEYWORD hard,nonn AUTHOR Ant King, Jan 25 2007 STATUS approved

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Last modified August 10 16:24 EDT 2022. Contains 356039 sequences. (Running on oeis4.)