It is well-known how to compute the density of square-free numbers, to get $$ \lim_{N\to\infty} \frac{\#\{ n \leq N : n \text{ square-free}\}}{N} = \frac{6}{\pi^2}.$$

What is the density of numbers such that both $n$ and $n+1$ are square-free? In other words, what is $$\lim_{N\to\infty} \frac{\#\{ n \leq N : n(n+1) \text{ square-free}\}}{N} $$ (if the limit exists)? I'm guessing this has been studied before. Does anyone have a textbook or paper reference?