...that is yet unsolved.
I joined almost at launch, and things were RADICALLY different back then in terms of the website's interface. One of the differences is a forums section (which was a pretty awesome feature, I don't know why anyone decided to take it down), and one of the threads contained a cool problem:
Diverges or Converges?
where denotes the number of positive integer divisors of N.
I have the answer. I also have two solutions. However, what is missing is a proof of the answer.
This seems to be a hard-core Number Theory problem. So whoever likes these, you're more than welcome to try this problem!
I shall post the answers I have if necessary. But first, give it your own shot.