SOLUTION: if 2^k-1 is a prime number,then show that 2^(k-1).(2^k-1)is a perfect number.

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Question 475362: if 2^k-1 is a prime number,then show that 2^(k-1).(2^k-1)is a perfect number.
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
Let denote the sum of factors of x. Since 2^k - 1 is prime, then


Also,


The sigma function is multiplicative, so

, hence it is a perfect number.