寻找前N个自然数的因子数的最佳算法是什么？

import math

def count_factors(num):
    count = 0
    sqrt_num = int(math.sqrt(num))
    for i in range(1, sqrt_num+1):
        if num % i == 0:
            count += 2
    if sqrt_num * sqrt_num == num:
        count -= 1
    return count

def find_top_n_factors(n):
    factors = []
    for num in range(1, n+1):
        factor_count = count_factors(num)
        factors.append((num, factor_count))
    factors.sort(key=lambda x: x[1], reverse=True)
    return factors[:n]

N = 10
top_n_factors = find_top_n_factors(N)
for num, factor_count in top_n_factors:
    print(f"Number: {num}, Factor Count: {factor_count}")