证明：存在常数 CCC，使对于所有正整数 nnn，有 ∑i=1n∑j=1nlcm(i,j)∑i=1n∑j=1ngcd(i,j)>C×(1+n1+lnn)2\frac{\sum_{i=1}^n\sum_{j=1}^n\operatorname{lcm}(i,j)}{\sum_{i=1}^n\sum_{j=1}^n\gcd(i,j)} > C \times \left (\frac{1+n}{1+\ln n}\right )^2∑i=1n∑j=1ngcd(i,j)∑i=1n∑j=1nlcm(i,j)>C×(1+lnn1+n)2
