= Prime-support equivalence relation
{title2=$m\sim n\iff\operatorname{rad}(m)=\operatorname{rad}(n)$}
Positive <integers> are equivalent when they have the same finite set of <prime factors>. Equivalently, each divides a positive power of the other. This <equivalence relation> is induced by the <radical of an integer>; its <equivalence classes> correspond to finite prime supports. The empty support gives the singleton $\{1\}$, and every nonempty support gives an infinite class by varying exponents.
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