Question 135
Find the smallest possible number of divisors a positive integer $n$ may have, which satisfies the following conditions:
1. $24 \mid n+1;$
2. The sum of the squares of all divisors of $n$ is divisible by $48$ (1 and $n$ are included).
1. $24 \mid n+1;$
2. The sum of the squares of all divisors of $n$ is divisible by $48$ (1 and $n$ are included).