Freaky Function!

Algebra Level 3

A function $f: \mathbb{N} \rightarrow \mathbb{N}$ is such that

1) $f(xy)= f(x)f(y)$

2) The function is strictly increasing.

3) $f(2)=2$

Find $\sum _{ k=1 }^{ 20 }{ f(k) }$