## Semidivisible numbers

### Problem 234

Published on Saturday, 28th February 2009, 01:00 am; Solved by 2251; Difficulty rating: 50%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 ?