# 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.

Title almost perfect number AlmostPerfectNumber 2013-03-22 17:41:51 2013-03-22 17:41:51 PrimeFan (13766) PrimeFan (13766) 4 PrimeFan (13766) Definition msc 11A05 least deficient number QuasiperfectNumber