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