GMAT Prep - PS Number Properties

Is the answer p-1?

Lets take 5 as an example(5 is a prime number).The positive integers less than 5 are 1,2,3,4. Each of these numbers is not a factor of 5. so f(p) in this case is 4. i.e.e p-1.
Let me know if this is correct.
thanks

Let us analyze it by plugging nos.

From Ques stem f(n)<1 and has no positive factor common other than1

Choice 1. p-1
if p is a prime no. f(p)=1 when p=2,
f(p)=2, when p=3
f(p)=4, when p=5

it seems to satisfy the above two conditions. Correct

choice 2. p-2
f(p)=0, when p=2
f(p)=1, when p=3
f(p)=3, when p=5

from the above we see that it doesnot satisfy the necessary condition stated. incorrect

Similarly we can plugin values and see that only choice A satisfies the necessary condition

Answer is P-1 (A)