Durfee's conjecture for isolated surface hypersurface singularities

Let $f\in\mathbb{C}[[x,y,z]]$ be an isolated hypersurface singularity. Let $\mu$ be its Milnor number and $p_g$ its geometric genus. Durfee's conjecture.

$$6p_g\leq\mu,$$

with equality only when $\mu=0$. This conjecture is presented as still open and is stronger than the $3/2$ quotient conjecture.