+487 If we let $f(n)$ denote the sum of all the positive divisors of the integer $n$, how many integers $i$ exist such that $1 \leq i \leq 2010$ and $f(i)=1+\sqrt{i}+i$?
+605 The LHS is an integer, so the RHS must be as well and conversely $i=n^2$ for integer $n$.
Then sum of divisors of $n^2$ is $n^2+n+1$ then use the divisor sum formula.
