Will someone help me with this problem. I'm struggling with it.

Define an equivalence relation R on the set P of positive integers by $\displaystyle mRn \Longleftrightarrow$ m and n have the same number of prime factors. Is there a function $\displaystyle f:P/R \rightarrow P/R \text{ such that } f([n]_R)=[3n]_R$ for each n?

I don't know how to show if this function exists or not. I just learned that a function is a relation such that if the ordered pair (x,y) and (x,y') are elements in R then, y=y'. I don't know how to apply that here. Please help.