Primitive abundant number

In math, a primitive abundant number is a special kind of abundant number. Its proper divisors, however, must all be deficient numbers(numbers whose sum of proper divisors are less than 2 times that number).
Example.
For example, 20 is a primitive abundant number because:
The first few primitive abundant numbers are 20, 70, 88, 104, 272, 304, 368, 464, 550, 572 ... 
The smallest odd primitive abundant number is 945.
Properties.
Every multiple of a primitive abundant number is abundant .
Every abundant number is a multiple of either a primitive abundant number or a multiple of a perfect number.
Every primitive abundant number is either a primitive semiperfect number or a weird number.
There is an infinite amount of primitive abundant numbers.