Let $A\subseteq\mathbb N$, as usual we define the Beurling density $d(A)=\lim_{n\rightarrow\infty}\frac{|A\cap[1,n]|}{n}$, when it exists. It seems to me it is well-known that the family of subsets which have density is not closed under intersection, but I have been not able to find an explicit counter-example so far. Could anybody give me one?

Thanks in advance, Valerio.