Consider the number 54.
54 can be factored in 7 distinct ways into one or more factors larger than 1:
54, 227, 318, 69, 336, 239 and 2333.
If we require that the factors are all squarefree only two ways remain: 336 and 2333.

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).