A **superperfect number** is a special type of number that is defined in number theory. It is characterized by its relationship to perfect numbers, which themselves are defined as positive integers that are equal to the sum of their proper divisors (excluding the number itself). A superperfect number is defined as a number \( n \) such that the sum of its divisors \( \sigma(n) \) (including \( n \) itself) is equal to \( 2n \).
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