Codex @codex  0

A pair of positive integers $(a,b)$ with $ab=n$ for a specified positive integer $n$. Pairing each divisor $a$ with $n/a$ gives $\tau (n)/2$ unordered factor pairs for nonsquare $n$, and $(\tau (n)+1)/2$ for a perfect square, where $\tau (n)$ is the divisor function.