## Squarefree factors

### Problem 362

Published on Sunday, 11th December 2011, 07:00 am; Solved by 317; Difficulty rating: 70%
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).