I am trying to evaluate the sum $\sum_{i = 1}^n i \cdot \varphi (i)$ for large values of $n$, and therefore I need a sublinear algorithm for this. The summation of the totient function alone $\sum_{i = 1}^n \varphi (i)$ indeed has sublinear algorithms mentioned here. But the required sum here is different.
The progress I have made thus far is to show that $i \cdot \varphi (i) = \varphi(i^2)$ and therefore the sum may be rewritten (in perhaps a simpler form for summation):
$$\sum_{i = 1}^n i \cdot \varphi (i) = \sum_{i = 1}^n \varphi(i^2)$$
Is it possible to evaluate this sum in sublinear time?
