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?
I did make a graph showing the chains for 1 through 100. It kind of looks fractal. I wouldn't know how to begin proving it or anything like that.
Now that you know which number<1000 takes the most steps, try to find the smallest numbers that take more steps.
Posted by Jer
on 2006-01-11 14:26:40