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, 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).

**
These problems are part of
Project Euler
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