  For $k \geq 2$, we consider the number $A_k(Z)$ of positive integers $n \leq
Z$ such that both $n$ and $n+1$ are $k$-free. We prove an asymptotic formula
$A_k(Z) = c_k Z + O(Z^{14/(9k)+\epsilon})$, where the error term improves upon
previously known estimates. The main tool used is the approximative determinant
method of Heath-Brown.
