So I've found that you can find the sum of $\sigma_0(n)$ by using:
$\sum_{i=1}^N \sigma_0(i) = \sum_{i=1}^N \lfloor \frac{N}{i} \rfloor$
or better yet:
$\sum_{i=1}^N \sigma_0(i) = \sum_{i=1}^f 2 * \lfloor \frac{N}{i} \rfloor - f^2$ where $f = \lfloor N^\frac{1}{2} \rfloor$
Is there a similarly useful expression for:
$\sum_{i=1}^N \sigma_0(i^2) = \space?$