Let $f(n)$ be the number of couples $(x, y)$ with $x$ and $y$ positive integers, $x \le y$ and the least common multiple of $x$ and $y$ equal to $n$.
Let $g$ be the summatory function of $f$, i.e.: $g(n) = \sum f(i)$ for $1 \le i \le n$.
You are given that $g(10^6) = 37429395$.
Find $g(2^N)$.