13. From the consecutive natural numbers $1,2,3, \cdots, 2014$, select $n$ numbers such that these $n$ numbers satisfy: taking any two of them, one will not be 5 times the other. Try to find the maximum value of $n$, and explain the reason.
【Key Points】Construction, Maximum Value
【Answer】 1679
【Explanation】Take as many numbers as possible
(1) $2014 \div 5=402 \cdots \cdots 4$, from 2014 to 403, there are $2014-402=1612$ numbers;
(2) $402 \div 5=80 \cdots \cdots 2$, from 402 to 81, no numbers are taken;
(3) $80 \div 5=16$, from 80 to 17, there are $80-16=64$ numbers;
(4) $16 \div 5=3 \cdots \cdots 1$, from 16 to 4, no numbers are taken;
(5) Finally, take $3, 2, 1$; $n=1612+64+3=1679$.