---
id: 5900f4d61000cf542c50ffe9
title: 'Problem 362: Squarefree factors'
challengeType: 5
forumTopicId: 302023
dashedName: problem-362-squarefree-factors
---

# --description--

Consider the number 54.

54 can be factored in 7 distinct ways into one or more factors larger than 1:

54, 2×27, 3×18, 6×9, 3×3×6, 2×3×9 and 2×3×3×3.

If we require that the factors are all squarefree only two ways remain: 3×3×6 and 2×3×3×3.

Let's call Fsf(n) the number of ways n can be factored into one or more squarefree factors larger than 1, so Fsf(54)=2.

Let S(n) be ∑Fsf(k) for k=2 to n.

S(100)=193.

Find S(10 000 000 000).

# --hints--

`euler362()` should return 457895958010.

```js
assert.strictEqual(euler362(), 457895958010);
```

# --seed--

## --seed-contents--

```js
function euler362() {

  return true;
}

euler362();
```

# --solutions--

```js
// solution required
```