I am struggling with solving the following equation for positive integers $k_1$ and $k_2$ in terms of $n\in \mathbb{Z}_+$ and $i,j\in \mathbb{Z}_+$:
$$n-1=\sum_{i\le k_1,j\le k_2}\sum_{\text{gcd}(i,j)=1}1.$$
Note that this equation can be interpreted also as
$n-1=\sum_{i\le k_1}\sum_{j\le k_2}\sum_{d\ge 1,d|\text{gcd}(i,j)}\mu(d)$
where $\mu$ is the Mobius function defined as
$\mu(n)=\begin{cases} 1 & \text{if $n$ is a square-free positive integer with an even number of prime factors}\\ -1 & \text{if $n$ is a square-free positive integers with an odd number of prime factors}\\ 0 & \text{if $n$ has a squared prime factor.} \end{cases}$