Euler #75

from math import gcd


def coprime(a, b, c):
    return gcd(a, b) == 1 and gcd(a, c) == 1 and gcd(b, c) == 1


sums, seen = [0]*1500001, []
for x in range(1, int(1500000 ** 0.5 + 2)):
    for y in range(x + 1, 10 ** 10):
        if not coprime(x ** 2 + y ** 2, 2 * x * y, y ** 2 - x ** 2):
            continue
        total = 2 * y ** 2 + 2 * x * y
        for z in range(1, 10 ** 10):
            new_total = total * z
            if new_total > 1500000:
                break
            sums[new_total] += 1
        if total > 1500000:
            break
print(sums.count(1))