The Briancon-Skoda number of analytic irreducible planar curves

The Briancon-Skoda number of a ring R is defined as the smallest integer k, such that for any ideal I\subset R and r\geq 1, the integral closure of I^{k+r-1} is contained in I^r. We compute the Briancon-Skoda number of the local ring of any analytic irreducible planar curve in terms of its Puiseux characteristics. It turns out that this number is closely related to the Milnor number.