I have been solving a problem and after much simplification I have been able to convert it of the below form and am unable to reduce it further.
$$\sum_{i=1}^n (-1)^i \phi(m*i) \left[\frac{n}{i}\right] $$
where $\phi(k)$ denotes Euler Totient Fucntion and [x] denotes Greatest Integer Function and m denotes a prime number
Here n is of the order $10^{9}$ so this must be solved either in O(constant) or O(logN).
Is it possible to reduce this furthur?
Thanks in advance :)))