Let $\sigma(n) $ denote the sum of positive divisors of a number $n $. A positive integer $N=2^rb $ is given,where $r $ and $b $ are positive integers and $b $ is odd. It is known that $\sigma(N)=2N-1$. Prove that $b$ and $\sigma (b) $ are coprime. Tuymaada Q6 Juniors