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?

Rather than checking all numbers, to see if they take more steps, try using a different step. For example, if checking numbers in the billions, don't check 1000000001, 1000000002, ..., etc, instead, check the evens, or even go further than that. Currently, I am checking for a 23 step number, and have gone, using a higher step, up to at least 65 billion. I say at least, because my computer is at home doing this, while I'm at school.

Posted by Justin on 2006-01-13 11:10:00