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
Canonical name	AlmostPerfectNumber
Date of creation	2013-03-22 17:41:51
Last modified on	2013-03-22 17:41:51
Owner	PrimeFan (13766)
Last modified by	PrimeFan (13766)
Numerical id	4
Author	PrimeFan (13766)
Entry type	Definition
Classification	msc 11A05
Synonym	least deficient number
Related topic	QuasiperfectNumber