Probability of Random Integer being Square-Free

Theorem
Let $a$ be an integer chosen at random.

The probability that $a$ is square-free is given by:
 * $P \left({\neg \exists b \in \Z: b^2 \mathrel \backslash a}\right) = \dfrac 1 {\zeta \left({2}\right)} = \dfrac 6 {\pi^2}$

where $\zeta$ denotes the zeta function.

The decimal expansion of $\dfrac 1 {\zeta \left({2}\right)}$ starts:
 * $\dfrac 1 {\zeta \left({2}\right)} = 0 \cdotp 60792 \, 71018 \, 54026 \, 6 \ldots$