Prime support of an integer ($P(n)=\{p\text{ prime}:p\mid n\}$)

The prime support of an integer $n>0$ is the finite set of its distinct prime factors. For example, $P(72)=P(36)=\{2,3\}$, $P(30)=\{2,3,5\}$ and $P(1)$ is the empty set. Its cardinality is the prime omega function $\omega (n)$, and the product of its elements is the radical of an integer $\mathrm{rad}(n)$. These are two different ways to summarize the same finite set: a count and a product.