A network diagram showing the orbits of numbers with starting values between 1-250, and path lengths of at least 10. Six cycles have been identified, and coloured.

My first attempt at a #DiscreteDynamicalSystem

Take a number, n
If (n-1) is prime then map n -> n^2
If (n-1) is composite then map n-> Aliquot sum of (n-1)
Numbers 1-19 all end in a cycle. I am not sure about 20.

eg. 6 -> 36 -> 13 -> 16 -> 9 -> 7 -> 6.

#mathsky
#recreationalmaths
#mathsart