TITLE: Using the Euler totient function for a large number
QUESTION [7 upvotes]: So I have a test in a couple of hours and I'm having trouble finding information on how to use the Euler totient function for a large number so I'm wondering if someone could give me step-by-step instructions? :)
Here's a sample question for the test:
Find $\psi(93296)$.
Could you also give instructions on finding the prime factorisation as well? I used an online calculator and it is $2^4 * 7^3 * 17$ but I wouldn't know how to calculate this.

REPLY [2 votes]: $ψ(93296)=ψ(2^4)\timesψ(7^3)\timesψ(17)$
        =$(2^4-2^3)\times(7^3-7^2)\times(17-1)$
        =$8\times294\times16$
        =$37632$