Primitive_abundant_number
Primitive abundant number
Abundant number whose proper divisors are all deficient numbers
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 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:
The smallest odd primitive abundant number is 945.
A variant definition is abundant numbers having no abundant proper divisor (sequence A091191 in the OEIS). It starts: