rotational dynamics - Acceleration of body rolling down inclined plane

Acceleration of a body rolling down an inclined plane is given by:

$$\frac{g\sin\theta}{1+\frac{k^2}{r^2}}$$

$g$=acceleration due to gravity

$\theta$=angle of inclined plane

$k$=radius of gyration

$r$=radius of abject

How come acceleration is independent of coefficient of friction of plane when friction itself is causing the torque? I am not able to understand this although I am able to derive the formula on my own.