Primitive abundant number

In mathematics a primitive abundant number is an abundant number whose proper divisors are all deficient numbers.

[1][2] For example, 20 is a primitive abundant number because: The first few primitive abundant numbers are: The smallest odd primitive abundant number is 945.

A variant definition is abundant numbers having no abundant proper divisor (sequence A091191 in the OEIS).

Every multiple of a primitive abundant number is an abundant number.

Every abundant number is a multiple of a primitive abundant number or a multiple of a perfect number.