For an integer $n\ge 4$, we define the lower prime square root of $n$, denoted by $\mathrm{lps}(n)$, as the largest prime $\le \sqrt{n}$ and the upper prime square root of $n$, $\mathrm{ups}(n)$, as the smallest prime $\ge \sqrt{n}$.

So, for example, $\mathrm{lps}(4)=2=\mathrm{ups}(4)$, $\mathrm{lps}(1000)=31$, $\mathrm{ups}(1000)=37$.
Let us call an integer $n\ge 4$ semidivisible, if one of $\mathrm{lps}(n)$ and $\mathrm{ups}(n)$ divides $n$, but not both.

The sum of the semidivisible numbers not exceeding $15$ is $30$, the numbers are $8$, $10$ and $12$.
$15$ is not semidivisible because it is a multiple of both $\mathrm{lps}(15)=3$ and $\mathrm{ups}(15)=5$.
As a further example, the sum of the $92$ semidivisible numbers up to $1000$ is $34825$.

What is the sum of all semidivisible numbers not exceeding $999966663333$?