Primes again 2

Algebra Level 5

\[\sum _{ \text{S has 4 divisors} } \frac { 1 }{ S^{ 2 } } =A\]

Find \(\left\lfloor 100000A \right\rfloor \).


You may use the approximations \[\begin{matrix} P(2)=0.452247 \\ P(4)=0.0769931 \\ P(6)=0.0170701 \end{matrix}\]

where \(P(n)\) is the prime zeta function, ie \(\displaystyle P(n)=\sum _{p \text{ prime} }{ { p }^{ -n } } \).

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