from functools import lru_cache
from lib_prime import prime_factors


@lru_cache(maxsize=200000)
def unique_factors(n: int) -> set[int]:
    return set(prime_factors(n))


def euler_127():
    c_max = 120000
    r = 0

    # for a in [5]:
    for a in range(1, c_max):
        fsa = unique_factors(a)
        # for b in [27]:
        for b in range(a + 1, c_max):
            if a + b > c_max:
                break
            c = a + b
            rad = 1

            do_continue = False
            for fa in fsa:
                rad *= fa
                if b % fa == 0:
                    do_continue = True
                    break
                if c % fa == 0:
                    do_continue = True
                    break
            if do_continue:
                continue
            if rad > c:
                continue

            do_continue = False
            fsb = unique_factors(b)
            for fb in fsb:
                rad *= fb
                if c % fb == 0:
                    do_continue = True
                    break
            if do_continue:
                continue

            if rad >= c:
                continue

            fsc = unique_factors(c)
            for fc in fsc:
                rad *= fc
            if rad >= c:
                continue

            # print(fsa, fsb, fsc)
            # print(a, b, c)
            r += c
    return r


if __name__ == "__main__":
    solution = euler_127()
    print("e127.py: " + str(solution))
    assert(solution == 18407904)