//Paste your solution here if you want to share it publiclydef order_by_factors_optimized(limit=100000, output_file=None): factor_counts = [0] * (limit + 1) for i in range(1, limit + 1): for j in range(i, limit + 1, i): factor_counts[j] += 1 numbers = list(range(1, limit + 1)) numbers.sort(key=lambda x: (-factor_counts[x], x)) file_handle = open(output_file, 'w') if output_file else None current_count = None for number in numbers: count = factor_counts[number] if current_count != count: if current_count is not None: line = "\n" print(line, end='') if file_handle: file_handle.write(line) current_count = count line = f"{number} : {count}" print(line) if file_handle: file_handle.write(line + "\n") if file_handle: file_handle.close() order_by_factors_optimized(100000, output_file='output.txt')