Untouchable numbers

While weird numbers are not equal to the sum of any of their divisors,untouchable numbers take it a step further. For a number to be untouchable, it must not be equal to the sum of the proper divisors of ANY number. A few untouchables are 2, 5, 52, and 88; in fact, 5 is thought to be the only odd untouchable number in existence (though it hasn’t been formally proven). There are an infinite number of untouchable numbers, meaning there is no such thing as the largest one.