Counting fractions in a range
Consider the fraction, n/d, where n and d are positive integers. If n < d and HCF(n,d)=1, it is called a reduced proper fraction.
If we list the set of reduced proper fractions for d ≤ 8 in ascending order of size, we get:
It can be seen that there are 3 fractions between 1/3 and 1/2.
How many fractions lie between 1/3 and 1/2 in the sorted set of reduced proper fractions for d ≤ 12,000?
考虑形如n/d的分数，其中n和d均为正整数。如果n < d且其最大公约数为1，则该分数称为最简真分数。
如果我们将d ≤ 8的最简真分数构成的集合按大小升序列出，我们得到：
将d ≤ 12,000的最简真分数构成的集合排序后，在1/3和1/2之间有多少个分数？