\(\sum\limits^N\sum\limits^N[gcd(X,Y)=1]\cdot \left [ \max\left ( \sum\limits^X \sum\limits^Y[gcd(x,y)=1]\cdot x , \sum\limits^X \sum\limits^Y[gcd(x,y)=1]\cdot y \right ) \leq N \right ]\)
\(\leq \sum\limits_{1\leq X,Y\leq N} \left [ \max\left ( \sum\limits^{+\infty}\mu(d)d \sum\limits^{X/d} \sum\limits^{Y/d}x , \sum\limits^{+\infty}\mu(d)d \sum\limits^{X/d} \sum\limits^{Y/d}y \right ) \leq N \right ]\)
\(\sum\limits_{1\leq X,Y\leq N}[XY\max(X,Y)\leq \Theta(N)] =O(n^\frac 23)\)
标签：right,gcd,limits,sum,leq,123,left From： https://www.cnblogs.com/1Liu/p/16748799.html