If we let \(f(n)\) denote the sum of all the positive divisors of the integer \(n\), how many integers \(i\) exist such that \(1 and \(f(i)=1+\sqrt{i}+i\)?

Please help!!

Sorry, something was messed up. I meant \(1 instead of \(1.

It seems like it's not letting me use LaTeX. What it's supposed to say is:

1 < i < 2010

There are 25 integers that work.

That answer is incorrect. The correct answer is 14.