# Mystical Summation that requires explaination

$\sum _{ { \sigma }_{ 0 }\left( n \right) \ge 8 }^{ }{ \frac { 1 }{ { n }^{ 2 } } } =A$

Find $$\displaystyle \left\lfloor 10000A \right\rfloor$$.

Inspiration

Bonus: Find the exact value

You may use the following approximations

$$\displaystyle { \pi }^{ 2 }\approx 9.8696044$$

$$\displaystyle P\left( 2 \right) \approx 0.4522474$$

$$\displaystyle P\left( 4 \right) \approx 0.0769931$$

$$\displaystyle P\left( 6 \right) \approx 0.0170700$$

$$\displaystyle P\left( 8 \right) \approx 0.0040614$$

$$\displaystyle P\left( 10 \right) \approx 0.0009936$$

$$\displaystyle P\left( 12 \right) \approx 0.0002460$$

Notation:

$$\displaystyle { \sigma }_{ 0 }\left( n \right)$$ is the divisor function, it counts the number of positive factors of a number.

$$\displaystyle P\left( x \right)$$ is the prime zeta function or $$\displaystyle P\left( n \right) =\sum _{ p\quad prime }^{ }{ \frac { 1 }{ { p }^{ n } } }$$

$$\displaystyle \left\lfloor x \right\rfloor$$ is the floor function.

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