Primitive Roots

We say that integer x, 0 < x < p, is a primitive root modulo odd prime p if and only if the set { (xⁱ mod p) | 1 <= i <= p-1 } is equal to { 1, ..., p-1 }. For example, the consecutive powers of 3 modulo 7 are 3, 2, 6, 4, 5, 1, and thus 3 is a primitive root modulo 7.
Write a program which given any odd prime 3 <= p < 65536 outputs the number of primitive roots modulo p.

Each line of the input contains an odd prime numbers p. Input is terminated by the end-of-file seperator.

For each p, print a single number that gives the number of primitive roots in a single line.

23
31
79

10
8
24