10 Sep
2008
10 Sep
'08
11:18 p.m.
Just for the fun of it, let's use Riemann's hypothesis. The proof that the proportion of squarefree numbers <= x is around 6/pi^2*x + O(sqrt(x)) is not too hard, if I remember correctly. Assuming the Riemann hypothesis to be true, we can use an equivalent formulation (which is given by formula (4) in http://mathworld.wolfram.com/MertensConjecture.html). This gives us that the desired quantity <= x is around 3/pi^2*x + O(x^(1/2 + e)). Stefan