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 $g({10}^{12})$.