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A127660
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Integers whose exponential aliquot sequences end in an exponential amicable pair.
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6
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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, 3907008, 3911796, 4122468, 4248552, 4275684
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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EXAMPLE
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a(11) = 1383732 because the eleventh integer whose exponential aliquot sequence ends in an exponential amicable pair is 1383732.
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MATHEMATICA
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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[ # ]]] &]
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 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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