  Let $A \subset {\mathbb Z}$ be a finite subset. We denote by $\mathcal{B}(A)$
the set of all integers $n \ge 2$ such that $|nA| > (2n-1)(|A|-1)$, where
$nA=A+\cdots+A$ denotes the $n$-fold sumset of $A$. The motivation to consider
$\mathcal{B}(A)$ stems from Buchweitz's discovery in 1980 that if a numerical
semigroup $S \subseteq {\mathbb N}$ is a Weierstrass semigroup, then
$\mathcal{B}({\mathbb N} \setminus S) = \emptyset$. By constructing instances
where this condition fails, Buchweitz disproved a longstanding conjecture by
Hurwitz (1893). In this paper, we prove that for any numerical semigroup $S
\subset {\mathbb N}$ of genus $g \ge 2$, the set $\mathcal{B}({\mathbb N}
\setminus S) $ is finite, of unbounded cardinality as $S$ varies.
