<|im_start|>system
You are a helpful assistant. You first think about the reasoning process in the mind and then provide the user with the answer. You should try to truely solve the question by yourself without cheating.  <|im_end|>
<|im_start|>user
 For a positive integer \( n \geq 2 \), let \(\alpha(n)\) denote the sum of all positive divisors of \( n \) (including 1 and \( n \)). Define a positive integer \( n \) as a "good number" if \(\gcd(n, \alpha(n)) = 1\). What is the maximum number of consecutive good numbers? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>
<|im_start|>assistant
Let me solve this step by step.
<think>
user
5
For a positive integer \( n \geq 2 \), let \(\alpha(n)\) denote the sum of all positive divisors of \( n \) (including 1 and \( n \)). Define a positive integer \( n \) as a "good number" if \(\gcd(n, \alpha(n)) = 1\). What is the maximum number of consecutive good numbers?
test