sum over primes less than 'x is there  a function $ f(x) $ so
$$ \sum_{p\le x}f(p)=S(x)$$
where $ S(x)=g(f(x), \pi(x) $
this means that the sum S(x) depends on the function $ f(x)$ but also on the prime number counting function 
the only case is $ f(x)=0$ but can be another alternatives ?
for example, the integral of a function $ \int f(x)dx =f(x) $ means that $ f(x)=e^{x} $
but how about a sum over primes which is equal to itself for a non zero function ??

Henry has a good example in the comments:
$$\sum_{p<x|\text{p is prime}}k = k\pi(x)$$
(where $\pi(x)$ is the prime counting function)
