  A curve $X$ is said to be of type $(N,\gamma)$ if it is an $N$--sheeted
covering of a curve of genus $\gamma$ with at least one totally ramified point.
A numerical semigroup $H$ is said to be of type $(N,\gamma)$ if it has $\gamma$
positive multiples of $N$ in $[N,2N\gamma]$ such that its $\gamma^{th}$ element
is $2N\gamma $ and $(2\gamma+1)N \in H$. If the genus of $X$ is large enough
and $N$ is prime, $X$ is of type $(N,\gamma)$ if and only if there is a point
$P \in X$ such that the Weierstrass semigroup at $P$ is of type $(N,\gamma)$
(this generalizes the case of double coverings of curves). Using the proof of
this result and the Buchweitz's semigroup, we can construct numerical
semigroups that cannot be realized as Weierstrass semigroups although they
might satisfy Buchweitz's criterion.
