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 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.

Posted by Steve Herman on 2015-01-26 08:51:40