  We investigate finitary functions from $\mathbb{Z}_{n}$ to $\mathbb{Z}_{n}$
for a squarefree number $n$. We show that the lattice of all clones on the
squarefree set $\mathbb{Z}_{p_1\cdots p_m}$ which contain the addition of
$\mathbb{Z}_{p_1\cdots p_m}$ is finite. We provide an upper bound for the
cardinality of this lattice through an injective function to the direct product
of the lattices of all $(\mathbb{Z}_{p_i}, \mathbb{F}_i)$-linearly closed
clonoids, $\mathcal{L}(\mathbb{Z}_{p_i}, \mathbb{F}_i)$, to the $p_i+1$ power,
where $\mathbb{F}_i = \prod_{j \in \{1,\dots,m\}\backslash
\{i\}}\mathbb{Z}_{p_j}$. These lattices are studied in the litterature and we
can find an upper bound for cardinality of them. Furthermore, we prove that
these clones can be generated by a set of functions of arity at most
$\max(p_1,\dots,p_m)$.
