Functions

Let $f$ be a polynomial function such that $\log _2(f(x))=\left(\log _2\left(2+\frac{2}{3}+\frac{2}{9}+\ldots \ldots \infty\right)\right) \cdot \log _3\left(1+\frac{f(x)}{f(1 / x)}\right), x>0$ and $f(6)=37$. Then $\sum\limits_{\mathrm{n}=1}^{10} f(\mathrm{n})$ is equal to $\_\_\_\_$ .