6. Choose $k$ different numbers from $1,2, \cdots, 13$, such that the difference between any two of these $k$ numbers is neither 5 nor 8. Then the maximum value of $k$ is $(\quad$.
(A) 5
(B)6
(C) 7
(D) 8
6. B.

Arrange these 13 numbers in a circle such that the difference between any two adjacent numbers is 5 or 8 (as shown in Figure 5). If more than 6 numbers are taken, there must be 2 numbers that are adjacent on the circle. On the other hand, 6 numbers that meet the condition can be taken (by selecting any 6 numbers that are not adjacent on the circle), thus, the maximum value of $k$ is 6.