Find the number of natural numbers $n$ such that $\log _ { 4 } 2 n ^ { 2 } - \frac { 1 } { 2 } \log _ { 2 } \sqrt { n }$ is a natural number not exceeding 40. [4 points]
Find the number of natural numbers $n$ such that $\log _ { 4 } 2 n ^ { 2 } - \frac { 1 } { 2 } \log _ { 2 } \sqrt { n }$ is a natural number not exceeding 40. [4 points]