Pro's square free

import math

def lessthan(a, b, c, d):
    """Is a/b < c/d?"""
    return a * d < b * c

n = 10000000
squares = {i * i for i in range(2, int(math.sqrt(n + 1)))}
square_frees = [1 for i in range(n + 1)]
for i in range(0, n + 1):
    if i in squares and square_frees[i] == 1:
        for j in range(i, n + 1, i):
            square_frees[j] = 0
square_frees[0] = 0
a, b = 1000000000, 1
A, B = 106, 176
for i in range(1, n + 1):
    square_frees[i] += square_frees[i - 1]
    if lessthan(square_frees[i], i, a, b):
        a, b = square_frees[i], i
    #print("i = {}, ratio = {}".format(i, square_frees[i] / i))

print("lowest ratio: {}/{} = {} from i = {}".format(a, b, a / b, b))
print("comparing with {}/{} = {}".format(A, B, A / B))
if lessthan(a, b, A, B):
    print("counterexample found")
else:
    print("no counterexample")