# The number of coprime integers at most $m$ and $n$

I am trying to estimate the asymptotics of the number $$N(m,n)$$ of coprime integers where one of the integers is at most $$m$$ and the other is at most $$n$$. What I obtained looks as follows: $$N(m,n) = \frac{6}{\pi^2}mn + O(\max(m,n) \log (\max(m,n)))$$ I wonder if there exists an estimation with a $$o(mn)$$ error term.

• With elementary functions, I guess. Otherwise you have the trivial $N(n,m)=N(n,m)+o(mn)$ – ajotatxe May 9 at 16:30