Divide by divisor

If f ( x ) f(x) is the greatest prime divisor of x x divided by the smallest prime divisor of x x , for what values of x x is f ( f ( x ) ) f\big(f(x)\big) defined?

For all values of x x When x x is 1 When x x is not 1 When x x is prime When x x is prime or 1 When x x is an integer power of a prime When x x is an integer power of a prime or 1 For no values of x x

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