[Dynamic Systems] Computing the orbit of a number

[the_green_book]

Homework Statement

Choose an even number in the interval [100,199] and compute its orbit under the proper divisor function.

Homework Equations

Proper Divisor Function = σ(n) = Sum of all divisors of n, excluding n

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.

 

[Dick]

Homework Statement

Choose an even number in the interval [100,199] and compute its orbit under the proper divisor function.

Homework Equations

Proper Divisor Function = σ(n) = Sum of all divisors of n, excluding n

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.

'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.