Sigma over Phi

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


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

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