Determine whether a given positive integer is a perfect number. A perfect number equals the sum of its proper divisors (all divisors excluding itself).
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A perfect number equals the sum of its proper divisors. The first few are 6, 28, 496, 8128. All known even perfect numbers have the form 2^(p−1)(2^p − 1) where 2^p − 1 is a Mersenne prime.
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