# Problem 234: Semidivisible numbers

![graphic](img234.gif)

For an integer n ≥ 4, we define the lower prime square root of n,
denoted by lps(n), as the largest prime ≤ √n and the upper prime square
root of n, ups(n), as the smallest prime ≥ √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 ?