On the Harborth constant of $C_3 \oplus C_{3p}

For a finite abelian group $(G,+, 0)$ the Harborth constant $g(G)$ is the smallest integer $k$ such that each squarefree sequence over $G$ of length $k$, equivalently each subset of $G$ of cardinality at least $k$, has a subsequence of length $\exp(G)$ whose sum is $0$. In this paper, it is established that $g(G)= 3n + 3$ for prime $n \neq 3$ and $g(C_3 \oplus C_{9})= 13$.