Following Sierpinski ´ [12], the positive integer n is called pseudo
perfect if n can be written as a sum
of some subset of its proper divisors. For example, 36 = 1+2+6+9+18, and so 36 is
pseudo perfect
but not perfect. In this paper, we study pseudoperfect numbers of
a very special kind.
We call n a
near-perfect number
if it is the sum of all of its proper divisors, except one of them. The missing divisor
d is termed redundant. Thus,