almost perfect number

An almost perfect number or least deficient number is a number $n$ whose proper divisors add up to just one less than itself. That is, $\sigma (n)-n=n-1$, with $\sigma (n)$ being the sum of divisors function. Currently, the only known almost perfect numbers are the integer powers of 2 (e.g., 1, 2, 4, 8, 16, 32, 64, 128, etc.) No one has been able to prove that there are almost perfect numbers of a different form.