Is any number one less than the sum of its proper divisors?

Question

I've been fascinated by perfect numbers ever since I learned about them, but I don't think 1 should be counted in the sum. Every integer is divisible by itself and 1, so why is the number itself excluded and not 1? Are there any numbers that are the sum of all their proper divisors excluding 1 (that is, they are 1 less than the sum of all the proper divisors)?

Answer 1

Jonathan Vos Post comments on OEIS033880, the abundance of numbers:

For no known n is a(n) = 1. If there is such an n it must be greater than $10^{35}$ and have seven or more distinct prime factors (Hagis and Cohen 1982).