If we let \(f(n)\) denote the sum of all the positive divisors of the integer \(n\), how many integers \(i\) exist such that \(1 \le i \le 2010\) and \(f(i) = 1 + \sqrt{i} + i\)?
Because of the sqrt(i) term, i must be a perfect square. There are 44 perfect squares in the range 1, 2, 3, ..., 2010, so there are 44 vaues of i.
