Definition:Divisor Count Function

Let $n$ be an integer such that $n \ge 2$.

The tau function $\tau \left({n}\right)$ is defined on $n$ as being the total number of positive integer divisors of $n$.

That is:
 * $\displaystyle \tau \left({n}\right) = \sum_{d \backslash n} 1$

where $\displaystyle \sum_{d \backslash n}$ is the sum over all divisors of $n$.