id	title	challengeType	forumTopicId	dashedName
5900f4d61000cf542c50ffe9	Problem 362: Squarefree factors	5	302023	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 \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);

function squarefreeFactors() {

  return true;
}

squarefreeFactors();

// solution required