number is a positive integer that cannot be expressed as the sum of all the proper divisors of any positive integer (including the untouchable
i. There is no untouchable number that is one more than a prime.
ii. Except number 5, there is no untouchable number that is
three more than a prime.
(In reply to re: Solution
by Kenny M)
Jer's proof goes in the right direction. We are asked to prove that p+1 IS NOT untouchable, so we have to produce a number whose proper divisors add to p+1.