Can anyone give an estimate (Upperupper bound or Lower Boundlower bound) for
$\sum_{\substack{d|P_r \\ \frac{\sqrt P_r}{2}< d <\sqrt P_r }} 1 $
when the number of divisors $d\mid P_r$ such that $\frac{\sqrt{P_r}}{2}< d < \sqrt{P_r}$, where $P_r$ is the product of firstthe $r$ smallest primes?