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Search: id:A127659
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| A127659 |
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Exponential amicable numbers. |
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+0
5
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| 90972, 100548, 454860, 502740, 937692, 968436, 1000692, 1106028, 1182636, 1307124, 1546524, 1709316, 2092356, 2312604, 2638188, 2820132, 2915892, 3116988, 3365964, 3720276, 3729852, 3911796, 4122468, 4275684, 4323564
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Union of A126165 and A126166. The first 10 terms of this sequence are the same as the first 10 terms of A127660.
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REFERENCES
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Hagis, Peter Jr.; Some Results Concerning Exponential Divisors, Internat. J. Math. & Math. Sci., Vol. 11, No. 2, (1988), pp. 343-350.
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LINKS
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Pedersen, Jan Munch, Tables of Aliquot Cycles.
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FORMULA
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Non e-perfect numbers for which A126164(A126164(n))=n.
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EXAMPLE
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a(5)=937692 because the fifth non e-perfect integer that satisfies A126164(A126164(n))=n is 937692
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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[ # ] &]
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CROSSREFS
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Cf. A126164, A126165, A126166, A127656, A127657, A127658, A127660, A051377.
Sequence in context: A075007 A015316 A127660 this_sequence A126165 A116097 A116122
Adjacent sequences: A127656 A127657 A127658 this_sequence A127660 A127661 A127662
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KEYWORD
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hard,nonn
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AUTHOR
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Ant King (mathstutoring(AT)ntlworld.com), Jan 25 2007
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