Find the largest positive integer $k$, such that $\mu(n+r)=0$ for all $1\leq r\leq k$ where $r,n$ are positive integers.
As far as I could make out, we need to find out the maximum range(if nay) of numbers where each has a square divisor.
I have gone through the theory of square-free numbers here and there, but could not proceed much.