Sigma Function of Prime Number
Let $n$ be a positive integer.
Let $\map \sigma n$ be the sigma function of $n$.
Therefore, the following suffices:
Suppose $n$ is a prime.
Therefore $\map \sigma n$, defined as the sum of the divisors of $n$, equals $n + 1$.
Suppose $n$ is not a prime.
As $n$ is composite:
- $\exists r, s \in \N: r, s > 1: r s = n$
Trivially, both $r$ and $s$ are divisors of $n$.
- $\map \sigma n \ge n + 1 + r + s > n + 1$