Sigma over Phi

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 \(\frac{\sigma(p)}{\phi(p)}\)?

Details and assumptions

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

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