# Problem 362: Squarefree factors
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).