The Stacks project

Exercise 111.49.7. Give an example of a Weil divisor $D$ on a variety which is not the Weil divisor associated to any Cartier divisor and such that $nD$ is NOT the Weil divisor associated to a Cartier divisor for any $n > 1$. (Hint: Consider a cone, for example $X : xy - zw = 0$ in $\mathbf{A}^4_ k$. Try to show that $D = [x = 0, z = 0]$ works.)