There are infinite such numbers, both even and odd. However Dickson proved that there are only a finite number of odd primitive abundant numbers with a given number of distinct prime factors. For example, there are only 8 odd primitive abundant numbers with 3 distinct prime factors, namely, 945, 1575, 2205, 7425, 78975, 131625, 342225, and 570375.

The first primitive abundant numbers are 12, 18, 20, 30, 42, 56, 66, 70, 78, 88, 102, 104, 114, 138, 174, 186, 196 more terms

A second definition of primitive numbers excludes also those that have perfect proper divisors, like all multiples of 6. The first such numbers are 20, 70, 88, 104, 272, 304, 368, 464, 550, 572, 650, 748, 836, 945, 1184, 1312, 1376, 1430, 1504, 1575, 1696, 1870, 1888, 1952, 2002.

Pictorial representation of remainders (mod 2, 3, ...,11) frequency. For a table of values and more details click here

A graph displaying how many primitive abundant numbers are multiples of the primes p from 2 to 71. In black the ideal line 1/p.