Question

Prove the following:
If k is a positive integer and (2^k)-1 is prime, then (2^(k-1))*((2^k)-1) is perfect.

A number n is perfect if the sum of all it's positive divisors (including 1 and itself) is 2n.

Answer 1

I feel like I should be using induction, but I'm not sure how to apply it.