If we let $f(n)$ denote the sum of all the divisors of the integer $n$, how many integers $i$ exist such that $1 \le i \le 2010$ and $f(i) = 1 + \sqrt{i} + i$?
How do I find the solution to this problem? Here are my thoughts.
Thought Process 1: Find all perfect squares (of primes) less than 2010. Would that be correct?
I think that the answer is 14 ?