Definition:Divisor Sum Function

Definition
Let $n$ be an integer such that $n \ge 1$.

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

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

Values
The sigma function for the first few positive integers is as follows:


 * $\begin{array} {r|r}

n & \sigma \left({n}\right) \\ \hline 1 & 1 \\ 2 & 3 \\ 3 & 4 \\ 4 & 7 \\ 5 & 6 \\ 6 & 12 \\ 7 & 8 \\ 8 & 15 \\ 9 & 13 \\ 10 & 18 \\ 11 & 12 \\ 12 & 18 \\ 13 & 14 \\ 14 & 24 \\ 15 & 24 \\ 16 & 31 \end{array}$

Also see

 * Definition:Divisor Function