Strange Number 2

Given two positive integers $A$ and $B$, let $f(A,B)$ be the number of positive integers $C$ that satisfy both of the following conditions.

$GCD(A,B) = GCD(A,C)$, $LCM(A,B) = LCM(B,C)$

Find the value of $\sum_{i=1}^N \sum_{j=1}^N f(i,j)$.

$GCD(A,B)$ is the greatest common divisor of $A$ and $B$, and $LCM(A,B)$ is the least common multiple of $A$ and $B$.

A single positive integer $N$ is given. $(1 \leq N \leq 10^9)$

Print the value of $\sum_{i=1}^N \sum_{j=1}^N f(i,j)$. Within the input range, this value is guaranteed to be less than $2^{63}$.