073.py

#!/usr/bin/python
# -*- coding: utf-8 -*-

#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:

#1/8, 1/7, 1/6, 1/5, 1/4, 2/7, 1/3, 3/8, 2/5, 3/7, 1/2, 4/7, 3/5, 5/8, 2/3, 5/7, 3/4, 4/5, 5/6, 6/7, 7/8

#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?

#Note: The upper limit has been changed recently.

#Answer:
	#7295372

from time import time; t=time()
from mathplus import gcd

D=12000

cnt = 0
for n in range(5, D+1):
    for m in range(n//3+1, (n+1)//2):
        if gcd(n, m) == 1: cnt += 1

print(cnt)#, time()-t