Frattini subgroup of a cyclic group which is not a p group for some prime p

What can you say about the frattini subgroup of a finite cyclic group which is not a p-group? I am just wandering do I need to check for each individual case or is there any general result for the same. As we know that, in a finite case frattini subgroup is the set of all non-generators of the group. Does this help? I would like to know a general way for seeing the frattini subgroup of finite cyclic group which is not a p-group.

The Frattini subgroup of a group is the intersection of all of its maximal subgroups. For a cyclic group $\mathbb Z/n\mathbb Z$, the subgroups are exactly $k\mathbb Z/n\mathbb Z\cong \mathbb Z/(n/k)\mathbb Z$ for $k\mid n$. Such subgroups are maximal if and only if $k$ is a prime. So, $$\Phi(\mathbb Z/n\mathbb Z)=\bigcap_{p\mid n}p\mathbb Z/n\mathbb Z=\left(\bigcap_{p\mid n}p\mathbb Z\right)/n\mathbb Z.$$ The intersection $a\mathbb Z\cap b\mathbb Z$ is $\operatorname{lcm}(a,b)\mathbb Z$. So, $$\bigcap_{p\mid n}p\mathbb Z=\left(\prod_{p\mid n}p\right)\mathbb Z.$$ Writing this product as $\operatorname{rad}(n)$ (the radical), we have $$\Phi(\mathbb Z/n\mathbb Z)=\operatorname{rad}(n)\mathbb Z/n\mathbb Z\cong \mathbb Z/\frac{n}{\operatorname{rad}(n)}\mathbb Z,$$ a cyclic group of order $n/\operatorname{rad}(n)$.