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A127658 Exponential aspiring numbers. 4
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; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Exponential aspiring numbers are those integers whose exponential aliquot sequences end in an e-perfect number, but that are not e-perfect numbers themselves.

REFERENCES

Hagis, Peter Jr.; Some Results Concerning Exponential Divisors, Internat. J. Math. & Math. Sci., Vol. 11, No. 2, (1988), pp. 343-350.

LINKS

Table of n, a(n) for n=1..37.

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(5)=2916 because the fifth non-e-perfect number whose exponential aliquot sequence ends in an e-perfect number is 2916.

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]]; Select[Range[25000], ExponentialPerfectNumberQ[Last[eTrajectory[ # ]]] && !ExponentialPerfectNumberQ[ # ]&]

CROSSREFS

Cf. A127656, A127657, A127659, A127660, A054979.

Sequence in context: A158408 A158409 A061044 * A318720 A137490 A129575

Adjacent sequences:  A127655 A127656 A127657 * A127659 A127660 A127661

KEYWORD

nonn

AUTHOR

Ant King, Jan 25 2007

STATUS

approved

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Last modified May 31 16:29 EDT 2020. Contains 334748 sequences. (Running on oeis4.)