Counting fractions

Consider the fraction, \( \frac{n}{d} \), 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 \( d \leq 8 \) in ascending order of size, we get:

\[ \frac{1}{8}, \frac{1}{7}, \frac{1}{6}, \frac{1}{5}, \frac{1}{4}, \frac{2}{7}, \frac{1}{3}, \frac{3}{8}, \frac{2}{5}, \frac{3}{7}, \frac{1}{2}, \frac{4}{7}, \frac{3}{5}, \frac{5}{8}, \frac{2}{3}, \frac{5}{7}, \frac{3}{4}, \frac{4}{5}, \frac{5}{6}, \frac{6}{7}, \frac{7}{8} \]

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 \( d \leq 1,000,000 \) ?