This is similar to an existing thread, but sufficiently different, I think.

For any positive integer n, let with and relatively prime. The question concerns and .

One result. The exact power of 2 that divides is floor(log_{2}(n))+1.

Here's the proof:

What else can one say about the sequence ? The exact power of 3 that divides seems to be an increasing sequence, but I can't find any closed formula as for 2. The exact power of 5 that divides is not even an increasing sequence.

The integers and get quite large. I know almost nothing about the .

, , , and are prime.

Java has a pretty sophisticated probalistic prime testing algorithm. Java says with probability greater than 1-one millionth that is prime; has 221 decimal digits.

(I inadvertenly attached a thumbnail and don't know how to delete it; ignore it.)