OK that's cool, I thought that would be it although I'm really surprised you managed to compute $\displaystyle \phi(7^3)$ using that definition!

Consider the nth power of a prime, $\displaystyle p^n$, what numbers less than this share a factor with $\displaystyle p^n$ ?

Firstly what are the factors of $\displaystyle p^n$ ? Clearly just 1 and $\displaystyle p$. So any number less than $\displaystyle p^n$ that share a factor must have p as a factor. Can you figure out how many such numbers there are? When you work this out, subtract this number from $\displaystyle p^n$ and you will have the result for $\displaystyle \phi(p^n) $

(Effectively what you have done, is instead of working out how many numbers are coprime, you have worked out how many are not coprime, and subtracted this from p^n)

This will give you a quick generel result for $\displaystyle \phi(p^n)$ and you can just change the n to a three to give you your answer.

Good luck, and let us know where you get stuck.