Who discovered/proved that there are about $$ \frac{x}{\zeta(2)} $$ squarefree numbers up to $x$, or (roughly) when was this first known? Today I think this is considered 'obvious', but I don't know if that was always the case.
Was this known before the Basel problem was solved (showing that the sum is $\pi^2/6$)? Perhaps it was known in the form $$ x\cdot \prod_{n\ge2}\left(1+\frac{\mu(n)}{n^2}\right) $$ ?