Bulbs left on after 100 rounds of toggling

A room has $100$ bulbs, all off, numbered $1$ to $100$. Person $j$ (for $j=1,\dots,100$) walks in and toggles every bulb whose number is a multiple of $j$. After all $100$ people have passed, how many bulbs are lit?

10. Bulb $i$ is toggled once per divisor of $i$, so it ends on exactly when $i$ has an odd number of divisors. Divisors pair up as $d\leftrightarrow i/d$ except when $i$ is a perfect square, and there are $10$ squares up to $100$.