BG-MO 2017 Problem 3

Let $M$ be a set of $2017$ positive integers. For any subset $A$ of $M$ we define $f(A) := \{x\in M\mid \text{ the number of the members of }A\,, x \text{ is multiple of, is odd }\}$ . Find the minimal natural number $k$ , satisfying the condition: for any $M$ , we can color all the subsets of $M$ with $k$ colors, such that whenever $A\neq f(A)$ , $A$ and $f(A)$ are colored with different colors.