Primitive abundant number
In mathematics a primitive abundant number is an abundant number whose proper divisors are all deficient numbers.
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. It starts:Properties
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.
Every primitive abundant number is either a primitive semiperfect number or a weird number.
There are an infinite number of primitive abundant numbers.
The number of primitive abundant numbers less than or equal to n is
