Mathematica 9 is now available
Services & Resources / Wolfram Forums
-----
 /
MathGroup Archive
2005
*January
*February
*March
*April
*May
*June
*July
*August
*September
*October
*November
*December
*Archive Index
*Ask about this page
*Print this page
*Give us feedback
*Sign up for the Wolfram Insider

MathGroup Archive 2005

[Date Index] [Thread Index] [Author Index]

Search the Archive

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


  • Prev by Date: Bug with Limit, Series and ProductLog ?
  • Next by Date: CategoryCounts
  • Previous by thread: Re: Bug with Limit, Series and ProductLog ?
  • Next by thread: CategoryCounts