Sigma over Phi

Number Theory Level 4

Let $\sigma(n)$ be the sum of positive divisors of an integer $n,$ and $\phi(n)$ the number of positive integers smaller than $n$ that are coprime to $n$ . If $p$ is a prime number, what is the maximum value of $\frac{\sigma(p)}{\phi(p)}?$

You may choose to read the following blog post on Euler's theorem.