Pick any whole number greater than 1.
1. Write down all of its proper divisors (including 1 and the number itself)
2. Add the digits of these divisors.
3. Use this sum to repeat steps 1 and 2 until your number does not change.
Must the process terminate?
At what number(s) can the process terminate at?
What numbers <1000 take the most steps to terminate?
(In reply to
Proof? by goFish)
I agree that this is the approach to a proof. In fact, 48 is the largest value for which f(n) > n. I'm not sure what the 7744 boundary means.
num3(2*3*5*7*11*13*17*19*23)
223092870 9594 279 47 12 19 11 3 4 7 8 15
^- 9594>7744
What I really want is an interesting way to graphically display the tree that this forms. I think it might look cool...perhaps fractal.
re: Proof?
