Almost perfect number

In mathematics, an almost perfect number (sometimes also called slightly defective or least deficient number) is a natural number "n" such that the sum of all divisors of "n" (the sum-of-divisors function "σ"("n")) is equal to 2"n" − 1, the sum of all proper divisors of "n", "s"("n") = "σ"("n") − "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 2"k" 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 <math>b+3 and such that and are both primes, then would be an odd weird number.