from lib_prime import prime_factors_count
from collections import defaultdict


def sum_factors(n: int, k: int) -> int:
    factors_num = defaultdict(int)
    for i in range(n - k + 1, n + 1):
        for factor, count in prime_factors_count(i).items():
            factors_num[factor] += count
    for i in range(2, k + 1):
        for factor, count in prime_factors_count(i).items():
            factors_num[factor] -= count
    return sum(factor * count for factor, count in factors_num.items())


def euler_231():
    assert sum_factors(10, 3) == 14
    return sum_factors(20 * 10**6, 15 * 10**6)


if __name__ == "__main__":
    solution = euler_231()
    print(f"e231.py: {solution}")
    # assert(solution == 0)