--description--

Consider the number 54.

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

$$54, 2 × 27, 3 × 18, 6 × 9, 3 × 3 × 6, 2 × 3 × 9 \text{ and } 2 × 3 × 3 × 3$$

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 $\sum Fsf(k)$ for $k = 2$ to $n$.

$S(100) = 193$.

Find $S(10\,000\,000\,000)$.

--hints--

squarefreeFactors() should return 457895958010.

assert.strictEqual(squarefreeFactors(), 457895958010);

--seed--

--seed-contents--

function squarefreeFactors() {

  return true;
}

squarefreeFactors();

--solutions--

// solution required