14. From the 200 positive integers $1, 2, \cdots, 205$, what is the maximum number of integers that can be selected such that for any three selected numbers $a, b, c (a < b < c)$, we have $a b \neq c$?
14. First, the 193 numbers $1, 14, 15, \cdots, 205$ satisfy the conditions of the problem.

In fact, if $a, b, c (a < b < c)$, then $a b \geqslant 14 \times 15 = 210 > c$.
On the other hand, consider the following 12 sets of numbers:
$(2, 25, 2 \times 25), (3, 24, 3 \times 24), \cdots$,
$(13, 14, 13 \times 14)$.
These 36 numbers are all distinct, and the smallest number is 2, while the largest number is $13 \times 14 = 182 < 205$. Therefore, the 3 numbers in each set cannot all be selected. Thus, if the selected numbers satisfy the conditions of the problem, the number of selected numbers does not exceed 205 $-12=193$ (numbers).

In summary, from $1, 2, \cdots, 205$, the maximum number of numbers that can be selected to satisfy the conditions of the problem is 193.