RS-SMO 2012 Problem 5

Let $\mathbb{K}$ be two-dimensional integer lattice. Is there a bijection $f:\mathbb{N} \rightarrow \mathbb{K}$ , such that for every distinct $a,b,c \in \mathbb{N}$ we have: $$\gcd(a,b,c)>1 \Rightarrow f(a),f(b),f(c) \text{ are not colinear? }$$