GCD Subsequences

Pantelija was given a sequence of positive integers $a_1, a_2, \ldots, a_N$. Let's define the *gcd value* of this sequence as the number of its non-empty contiguous subsequences with greatest common divisor strictly greater than $1$. The greatest common divisor of any contiguous subsequence $a_l, a_{l+1}, \ldots, a_r$ ($1 \le l \le r \le N$) is the greatest positive integer which divides each elem