Abundant number

An abundant number is a number ${\displaystyle n}$ for which its sum of divisors, excluding itself, is greater than ${\displaystyle 2n}$. 12 is an abundant number because ${\displaystyle 1+2+3+4+6+12>24}$. 18 is also an abundant number because ${\displaystyle 1+2+3+6+9+18>36}$. The series is in the Online Encyclopedia of Integer Sequences (Sloane) as A005101. 120 is considered a super abundant number since the sum of its divisors equals exactly twice the number. 945 is the first odd abundant number. The smallest odd abundant numbers that end in 1, 3, 7, and 9, are 81081, 153153, 207207, and 189189, respectively.

If a number is not abundant, it is called either deficient or perfect.