13. Color $2,3, \cdots, 9$ in one of three colors: red, green, or blue, such that each number and its divisors have different colors. There are ( ) different ways to color them.
(A) 144
( B) 216
(C) 256
(D) 384
(E) 432
13. E.

The first step, color the numbers $2$, $4$, and $8$ with different colors, which has $3 \times 2 \times 1=6$ different coloring methods;

The second step, color the numbers $5$ and $7$, which has $3 \times 3=9$ different coloring methods;

The third step, color the number 6, since it must be a different color from number 2, there are 2 different coloring methods;

The fourth step, color the number 3, since it must be a different color from number 6, there are 2 different coloring methods;

The fifth step, color the number 9, since it must be a different color from number 3, there are 2 different coloring methods;
Therefore, there are $6 \times 9 \times 2 \times 2 \times 2=432$ different coloring methods.