TITLE: Kindda-Perfect number: Is there a sequence of numbers which are equal to the sum of its proper divisors excluding itself as well as 1?
QUESTION [6 upvotes]: Perfect number is a positive integer that is equal to the sum of its proper divisors. The smallest perfect number is 6, which is the sum of 1, 2, and 3.
Is there a sequence of numbers which are equal to the sum of its proper divisors excluding itself as well as 1?
If yes, what are they called? Name first few numbers in the sequence.
Is there a general formula for them?
Please provide with some link to read more.

REPLY [20 votes]: Such an abundant number with abundance 1 is called a quasiperfect number (which is a more professional way to say "kindda-perfect"). None have been found, according to Wikipedia. This 1982 article says that if a quasiperfect number exists, it must be an odd square number greater than $10^{35}$ and have at least seven distinct prime factors. A recent article on this topic is here.