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Search: id:A127658
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| A127658 |
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Exponential aspiring numbers. |
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+0
5
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| 900, 1352, 1728, 2880, 2916, 3000, 3750, 4356, 5292, 6480, 6760, 8100, 8640, 9464, 9900, 10404, 10648, 11700, 12000, 12096, 13500, 14580, 14872, 15300, 15552, 15876, 16000, 16200, 16224, 17100, 17836, 18252, 19008, 19044, 20160, 20412, 20700
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Exponential aspiring numbers are those integers whose exponential aliquot sequences end in an e-perfect number, but that are not e-perfect numbers themselves.
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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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EXAMPLE
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a(5)=2916 because the fifth non e-perfect number whose exponential aliquot sequence ends in an e-perfect number is 2916
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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]]; Select[Range[25000], ExponentialPerfectNumberQ[Last[eTrajectory[ # ]]] && !ExponentialPerfectNumberQ[ # ]&]
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CROSSREFS
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Cf. A127656, A127657, A127659, A127660, A054979.
Sequence in context: A063878 A063167 A061044 this_sequence A137490 A129575 A074853
Adjacent sequences: A127655 A127656 A127657 this_sequence A127659 A127660 A127661
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KEYWORD
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nonn
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AUTHOR
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Ant King (mathstutoring(AT)ntlworld.com), Jan 25 2007
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