Toggled switches after 100 passes

A row of $100$ switches all start in the left position. Person $1$ toggles every switch, person $2$ toggles switches $2,4,6,\dots$, person $3$ toggles every third switch, and so on up to person $100$, who toggles only switch $100$. How many switches end in the right position?

10. Switch $n$ is toggled once for each divisor of $n$, so it ends on the right exactly when $n$ has an odd number of divisors. Divisors pair up as $d$ and $n/d$ except when $n$ is a perfect square, and there are $10$ squares up to $100$.