Definition:Sigma Function

Definition

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

The sigma function $\sigma \left({n}\right)$ is defined on $n$ as being the sum of all the positive integer divisors of $n$.

That is:

$\displaystyle \sigma \left({n}\right) = \sum_{d \backslash n} d$

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

Sources

• George F. Simmons: Calculus Gems (1992), Chapter $\text {B}.2$