Some, but not all, of the first \(11\) positive integers is called strange. Here are some details:
If a number \(n\) is strange (\(1\leq n\leq 11\)), then \(12-n\) is also strange.
If a number is strange, then the positive divisors of the numbers are strange numbers.
At least one of the strange numbers is even.
If there are \(k\) number of strange numbers, then \(11-k\) is not a strange number.
Not all integers between \(1\) and \(11\) are strange.
What is the sum of the strange numbers?