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A positive integer n is called a perfect number if it is equal to the sum of all of its positive divisors, excluding n itself. Examples are 6=1+2+3, 28=1+2+4+7+14. An integer k is an even perfect number if and only if it has the form 2^(n1)(2^n1) and 2^n1 is prime. In that case 2^n1 is called a Mersenne prime and n must be prime. It is unknown whether there exists an odd perfect number. 
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