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Generating unitary aliquot cycles

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

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)
and

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

For example

In[33]:=
Trajectory[866]
Out[33]=
{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

Tony

Any


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