Pairs of Integers whose Product with Divisor Count are Equal

Theorem
Let $\tau \left({n}\right)$ denote the $\tau$ function: the number of divisors of $n$.

The following pairs of integers $T$ have the property that $m \tau \left({m}\right)$ is equal for each $m \in T$:
 * $\left\{ {18, 27}\right\}$
 * $\left\{ {24, 32}\right\}$
 * $\left\{ {56, 64}\right\}$