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.