MathNet 2011 Question 55

Let $a_n = C_{200}^n \cdot (\sqrt[3]{6})^{200-n} \cdot \left(\frac{1}{\sqrt{2}}\right)^n$ $(n = 1, 2, \dots, 95)$. Then the number of terms that are integers in $\{a_n\}$ is ______.