A perfect number is a positive integer n that equals the sum of all divisors less than n$.$ For example, $6$ is a perfect number because $6=1+2+3.$ Perfect numbers are related to Mersenne primes in that if p is a prime and pow $(2,$ p$)1$ is a prime, then pow $(2,$ p $1)($pow $(2,$ p$)1)$ is a perfect number.

write a Python function that proves this claim for all prime numbers n less than $12.$ Your program should$$check if n is prime and if so$,$ output n$,$ pow $(2,$n $1)($pow $(2,$n$)1)$ and also all divisors of pow $(2,$n $1)($pow $(2,$n$)1)$ to prove that pow $(2,$n $1)($pow $(2,$n$)1)$ is a perfect number.