An abundant number, sometimes also called an excessive number, is a positive integer n for which s(n) congruent σ(n) - n>n, where σ(n) is the divisor function and s(n) is the restricted divisor function. The quantity σ(n) - 2n is sometimes called the abundance. A number which is abundant but for which all its proper divisors are deficient is called a primitive abundant number. The first few abundant numbers are 12, 18, 20, 24, 30, 36, ... (OEIS A005101).
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