Almost perfect number
In mathematics, an almost perfect number is a natural number n such that the sum of all divisors of n is equal to 2n − 1, the sum of all proper divisors of n, s = σ − n, then being equal to n − 1. The only known almost perfect numbers are powers of 2 with non-negative exponents. Therefore the only known odd almost perfect number is 20 = 1, and the only known even almost perfect numbers are those of the form 2k for some positive number k; however, it has not been shown that all almost perfect numbers are of this form. It is known that an odd almost perfect number greater than 1 would have at least six prime factors.
If m is an odd almost perfect number then is a Descartes number. Moreover if a and b are positive odd integers such that and such that and are both primes, then would be an odd weird number.
