Create a function that takes a number max_den and returns the total number of fully simplified proper fractions that exist with denominator less than or equal to max_den.
You only need to return the number of fractions; NOT the fractions themselves. In the examples below, I list the fractions simply for your reference.
sim_prop_frac(10) ➞ 31
# 1/2, 1/3, 2/3, 1/4, 3/4, 1/5, 2/5, 3/5, 4/5, 1/6, 5/6, 1/7, 2/7, 3/7, 4/7, 5/7, 6/7, 1/8, 3/8, 5/8, 7/8, 1/9, 2/9, 4/9, 5/9, 7/9, 8/9, 1/10, 3/10, 7/10, 9/10
sim_prop_frac(7) ➞ 17
# 1/2, 1/3, 2/3, 1/4, 3/4, 1/5, 2/5, 3/5, 4/5, 1/6, 5/6, 1/7, 2/7, 3/7, 4/7, 5/7, 6/7
A fully simplified proper fraction is a fraction where both the numerator and denominator share no common factors besides 1 and the fraction is less than 1.