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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.

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

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