login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Table of n, a(n) for n=1..25.

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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