GCD Limit

For a sequence $A = (A_1, A_2, \ldots, A_N)$, we define $f(A)$ in the following way: - Let $P_i = \gcd(A_1, A_2, \ldots, A_i)$ - $f(A) = $ number of indices $i$ ($2 \le i \le N$) such that $P_i \ne P_{i - 1}$. --- Given an integer $M$, define $g(N)$ as the **expected value** of $f(A)$ when $A$ is uniformly randomly selected among all $M^N$ arrays satisfying the following conditions: - $|A| = N