σk(ij)=∑x∣i∑y∣j[gcd(x,y)=1](xjy)k\sigma_{k}(ij) = \sum_{x | i}\sum_{y | j} [\gcd(x, y) = 1] \left( \dfrac{xj}{y} \right) ^ kσk(ij)=∑x∣i∑y∣j[gcd(x,y)=1](yxj)k
