---
id: 5900f4571000cf542c50ff69
title: 'Problem 234: Semidivisible numbers'
challengeType: 5
forumTopicId: 301878
dashedName: problem-234-semidivisible-numbers
---

# --description--

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

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?

# --hints--

`semidivisibleNumbers()` should return `1259187438574927000`.

```js
assert.strictEqual(semidivisibleNumbers(), 1259187438574927000);
```

# --seed--

## --seed-contents--

```js
function semidivisibleNumbers() {

  return true;
}

semidivisibleNumbers();
```

# --solutions--

```js
// solution required
```