Let $\tau(n)$ be the number of positive divisors of $n\in \mathbb{N}$.

Is it possible to get some good estimate for the sum $\sum_{n\le x} \frac{n}{\tau(n)}$?

I know that the sum is $\mathcal O(x^2)$ but I was hoping for something better for example $\sum_{n\le x} \frac{n}{\tau(n)}=c\cdot x^2+\mathcal O(x^{small power})$.

Of course this may not be true, but I think it is a safe guess.

I tried partial summation but it did not help.