Question

How many positive integers n less than 1000, have the property that the number of positive integers less than n which are coprime to n, is exactly n/3 ?

Answer 1

Here is the Universe: 1, 2, 3, 4, ..., 999

1
Positive integers less than 1 -- 0 -- That's no good.

2
Positive integers less than 2 -- 1
Is 1 coprime to 2?

Please provide your definition if "coprime".