Primitive abundant number

For example, 20 is a primitive abundant number because:

The sum of its proper divisors is 1 + 2 + 4 + 5 + 10 = 22, so 20 is an abundant number.
The sums of the proper divisors of 1, 2, 4, 5 and 10 are 0, 1, 3, 1 and 8 respectively, so each of these numbers is a deficient number.

The first few primitive abundant numbers are:

20, 70, 88, 104, 272, 304, 368, 464, 550, 572 ... (sequence A071395 in the OEIS)

The smallest odd primitive abundant number is 945.

A variant definition is abundant numbers having no abundant proper divisor, which also include divisors that are perfect numbers. It starts:

12, 18, 20, 30, 42, 56, 66, 70, 78, 88, 102, 104, 114 ... (sequence A091191 in the OEIS)

v t e Divisibility-based sets of integers
Overview	Integer factorization Divisor Unitary divisor Divisor function Prime factor Fundamental theorem of arithmetic
Factorization forms	Prime Composite Semiprime Pronic Sphenic Square-free Powerful Perfect power Achilles Smooth Regular Rough Unusual
Constrained divisor sums	Perfect Almost perfect Quasiperfect Multiply perfect Hemiperfect Hyperperfect Superperfect Unitary perfect Semiperfect Practical Descartes Erdős–Nicolas
With many divisors	Abundant Primitive abundant Highly abundant Superabundant Colossally abundant Highly composite Superior highly composite Weird
Aliquot sequence-related	Untouchable Amicable (Triple) Sociable Betrothed
Base-dependent	Equidigital Extravagant Frugal Harshad Polydivisible Smith
Other sets	Arithmetic Deficient Friendly Solitary Sublime Harmonic divisor Refactorable Superperfect

References