[Perfect number](https://www.britannica.com/topic/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.



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?
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](https://en.wikipedia.org/wiki/Quasiperfect_number). This [1982 article](https://www.cambridge.org/core/journals/journal-of-the-australian-mathematical-society/article/some-results-concerning-quasiperfect-numbers/773348EC71E156E2E460DCC03D55030D) 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.](https://arxiv.org/abs/1610.01063)


