How to show that
$$
\sum\_{n=2}^\infty \frac{\sin{(nx)}}{\log n}
$$
not the Fourier series of any function?

I have shown that the series is convergent by Dirichlet test.

Let $a(n)=\frac{1}{\log n}$.
What is $\sum (a(n))^2$, to apply Parseval's theorem?