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Generating unitary aliquot cycles

  • To: mathgroup at
  • Subject: [mg61410] Generating unitary aliquot cycles
  • From: "Tony King" <mathstutoring at>
  • Date: Tue, 18 Oct 2005 02:45:02 -0400 (EDT)
  • Sender: owner-wri-mathgroup at

I would like to mimic the operation of the function AliquotCycle, accessed 
from the NumberTheory package, but for unitary divisors instead of normal 
divisors. The functions that I have been using are

UnitaryDivisorSigma[k_, n_Integer] :=
Times @@ (1 + (Power @@@ FactorInteger[n])^k)

g[n_] := If[n > 0, UnitaryDivisorSigma[1, n] - n, 0];
Trajectory[n_] := Most[NestWhileList[g, n, UnsameQ, All]]

For example

{866, 436, 114, 126}

returns the unitary aliquot sequence that terminates in the unitary amicable 
pair 114,126

I need a function UnitaryAliquotCycle that will output just the periodic 
part ({114,126} from an input of 866), and will similarly output all larger 
(or smaller) unitary sociable cycles in precisely the same way that 
AliquotCycle does.

Any assistance would be most appreciated



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