Chef and Moves of GCD

You are given an integer $N$. Consider an integer $X$ $(1\le X \le N)$. In one move, you have to: - Randomly pick an integer $P (1 \le P \le N)$; - Set the value of $X$ to [gcd](https://en.wikipedia.org/wiki/Greatest_common_divisor)$(X, P)$. Let, $E(X, N)$ denote the [expected number](https://en.wikipedia.org/wiki/Expected_value) of moves required to make $X = 1$. Find the value of $E(X, N)$ f