problem 72 // project euler

Counting fractions

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 21 elements in this set.

How many elements would be contained in the set of reduced proper fractions for d ≤ 1,000,000?

分数计数

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：

可以看出该集合中共有21个元素。

d ≤ 1,000,000的最简真分数构成的集合中共有多少个元素？