= Prime support of an integer
{title2=$P(n)=\{p\text{ prime}:p\mid n\}$}
= Prime supports of an integer
{synonym}
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> $\operatorname{rad}(n)$. These are two different ways to summarize the same <finite set>: a count and a <product>.
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