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 2n − 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 (sequence A000079 in the OEIS).

It is known that an odd almost perfect number greater than 1 would have at least six prime factors.

and such that 4m − a and 4m + b are both primes, then m(4m − a)(4m + b) would be an odd weird number.

[4] This number theory-related article is a stub.