Is there a name for this type of integer? An integer $n$ such that $\exists$ at least one prime $p$ such that, $p|n$ but $p^2$ does not divide $n$.
i.e. : an integer with at least one prime that has a single power in the prime factorization.
Do these numbers have a special name, and have they been studied?

These are sometimes called weak numbers, presumably because not weak naturals are precisely the powerful naturals. However the weak terminology does not appear to be anywhere near as widely used as is the powerful terminology (e.g. Granville and Ribenboim use "not powerful"). I also recall seeing other names besides weak (e.g. impotent).
