from lib_prime import prime_factors


def radical(n: int) -> int:
    fs = prime_factors(n)
    r = 1
    for f in set(fs):
        r *= f
    return r


def euler_124():
    assert radical(504) == 42
    xs = []
    for n in range(1, 100001):
        xs.append((radical(n), n))
    xs = sorted(xs)
    return xs[10000 - 1][1]


if __name__ == "__main__":
    solution = euler_124()
    print("e124.py: " + str(solution))
    assert(solution == 21417)