An untouchable number is a number that is not the sum of the proper divisors (the factors of a number except for itself) of any number.

5 is untouchable because 1 is a proper divisor of any number, and the only way to write 5 as a sum of positive integers including 1 is 1 + 4. But any number with 4 as a factor also has two as a factor, so its proper divisors will add to at least 7.

5 is the only odd number known to be untouchable, while there are infinitely many untouchable numbers in total.