Question

If (n) = 2n+1, prove that n is a square of an odd integer

Answer 1

Prove that if σ(n)=2n+1σ(n)=2n+1 then nn is an odd perfect square.

(Here, σ(n)σ(n) is the sum of the positive divisors of nn including 1 and nn itself.)

As I know, this nn is a quasiperfect number, and I just proved that nn is a perfect square or n2n2 is a perfect square.