\begin{definition}[Definition:Divisor Counting Function]
Let $n$ be an integer such that $n \ge 1$.
The '''divisor counting function''' is defined on $n$ as being the total number of positive integer divisors of $n$.
It is denoted on {{ProofWiki}} as $\sigma_0$ (the Greek letter '''sigma''').
That is:
:$\ds \map {\sigma_0} n = \sum_{d \mathop \divides n} 1$
where $\ds \sum_{d \mathop \divides n}$ is the sum over all divisors of $n$.
\end{definition}