An untouchable number is a positive integer that cannot be expressed as the sum of all the proper divisors of any positive integer (including the untouchable number itself).

Prove:
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 Solution by Jer)

Not sure I understand.
Don't you have to prove the the number p+1 itself cannot be expressed as the sum of the divisors of any other positive integer?  Looks like you are proving that p+1 is a sum that validates p^2 to be not untouchable?

Or am I mistaken?

Posted by Kenny M on 2015-01-25 17:24:57