  Let $(X,0)\subset (\mathbb{C}^n,0)$ be an irreducible weighted homogeneous
singularity curve and let $f:(X,0)\to(\mathbb{C}^2,0)$ be a map germ finite,
one-to-one and weighted homogeneous with the same weights of $(X,0)$. We show
that $\mathscr{A}_e$-$codim(X,f)=\mu_I(f)$, where $\mathscr{A}_e$-$codim(X,f)$
is the $\mathscr{A}_e$-codimension, i.e., the minimum number of parameters in a
versal deformation and $\mu_I(f)$ is the image Milnor number, i.e., the number
of vanishing cycles in the image of a stabilisation of $f$.
