Why Even Almost Perfect Number should not be Divisible by 3? A non-Almost Perfect Criterion for Even Positive Integers n ≠ 2k

Two of the oldest open problems in elementary number theory are (1) to find a quasi-perfect number and (2) to show that only numbers of the form 2(k), k is an element of Z(+) are almost perfect. A positive integer is quasi perfect if the sum of its positive divisors sigma(n) is equal to 2n + 1 where as n is almost perfect if sigma(n) is equal to2n - 1.In 1951, Cattaneo showed that quasi perfect numbers cannot be even. Recently, Antalan (2013) showed that almost perfect numbers not of the form 2(k) must be of the form 2(x)b(2) where x is an element of Z(>= 0) and b is an odd composite positive integer. Here we give sufficient non - almost perfect criterion for even positive integers n(e) of the form 2(x)b(2). Particularly we show that n(e) is automatically not an almost perfect number if it is divisible by 2(x) and a prime <= 2(x+1) - 1. Lastly we state a problem on almost perfect numbers related to what Cattaneo did on quasi perfect number.