Semidivisible numbers

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

So, for example, $lps(4) = 2 = ups(4)$, $lps(1000) = 31, ups(1000) = 37$. Let us call an integer $n ≥ 4$ semidivisible, if one of $lps(n)$ and $ups(n)$ 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 $lps(15) = 3$ and $ups(15) = 5$. 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 $999966663333$ ?