Let for a differentiable function $f : ( 0 , \infty ) \rightarrow R , f ( x ) - f ( y ) \geq \log _ { e } \left( \frac { x } { y } \right) + x - y , \forall x , y \in ( 0 , \infty )$. Then $\sum _ { n = 1 } ^ { 20 } f ^ { \prime } \left( \frac { 1 } { n ^ { 2 } } \right)$ is equal to