\begin{definition}[Definition:Divisor Sum Function]
Let $n$ be an integer such that $n \ge 1$.
The '''divisor sum function''' $\map {\sigma_1} n$ is defined on $n$ as being the sum of all the positive integer divisors of $n$.
That is:
:$\ds \map {\sigma_1} n = \sum_{d \mathop \divides n} d$
where $\ds \sum_{d \mathop \divides n}$ is the sum over all divisors of $n$.
\end{definition}