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[Dynamic Systems] Computing the orbit of a number

  1. May 6, 2013 #1
    1. The problem statement, all variables and given/known data
    Choose an even number in the interval [100,199] and compute its orbit under the proper divisor function.


    2. Relevant equations
    Proper Divisor Function = σ(n) = Sum of all divisors of n, excluding n


    3. The attempt at a solution
    I am unsure what it means by "compute the orbit" of a number. I assumed that it meant that I had to evaluate the number for the given function. Doing that I have:

    Chosen number = 138

    σ(138) = 1 + 2 + 3 + 6 + 23 + 46 + 69 = 150

    I am just not sure if that is what the question is asking. For anyone that has done orbits, is this essentially what I have to do?

    Thank you for your assistance.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. May 6, 2013 #2

    Dick

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    Science Advisor
    Homework Helper

    'Orbit' means once you have found σ(138)=150, you then find σ(150)=222. Then find σ(222) and keep on iterating the σ function until you get some sort of pattern. You may have made an unfortunate choice of even integer. It takes a very long time to do anything interesting except get larger. See, https://sites.google.com/site/robertharamoto/Home/programming/numbers/aliquot-sequence if you want to see someone elses experiments with this problem.
     
    Last edited: May 6, 2013
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