I believe its A...p-1. If a number is prime, its only factors are 1 and itself. Therefore, if p is a prime, any number less p will not be a factor of p. So, each of the p-1 integers less than p will have no factor in common with p other than 1, which implies that f(p) = p-1.

As an example, consider the prime number 7. There are 6 integers less than 7, none of which share any of the factors of 7 except 1 so f(7) = 6