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The following fact is stated in the comments-section of sequence A013928 in the OEIS.

Let $C$ be the $n$-by-$n$ matrix whose $(i,j)$-entry is one if $\gcd(i,j)=1$ and zero otherwise.

It is claimed that $\text{rank}(C) = Q(n+1)$, where $Q(n)$ denotes the number of squarefree integers less than $n$.

Looking for a reference on this claim (proving the claim is not an issue) and whether this matrix has been studied previously.

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