OK that's cool, I thought that would be it although I'm really surprised you managed to compute

using that definition!

Consider the nth power of a prime,

, what numbers less than this share a factor with

?

Firstly what are the factors of

? Clearly just 1 and

. So any number less than

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

and you will have the result for

:) (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

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.