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  "body": "\n## Definition\n\nA positive integer $n$ is abundant if the sum of its positive divisors other than $n$ is greater than $n$.\nEquivalently, $\\sigma(n) \u003e 2n$, where $\\sigma$ is the [[sum of divisors|009QCP5T3Z]].\n\n## Remarks\n\nThe smallest abundant number is $12$, since $1 + 2 + 3 + 4 + 6 = 16 \u003e 12$.\nThe smallest odd abundant number is $945$.\nEach multiple $kn$ with $k \\ge 2$ of a [[perfect number|0SB7Q8SYSF]] $n$ is abundant.\n\n## Explanations\n\n### L1 human\n\nAn abundant number has \"too many\" divisors: its smaller divisors add up to more than the number.\nCompare with [[perfect numbers|0SB7Q8SYSF]], where the sum is equal, and [[deficient numbers|0G01TS1RRP]], where it is smaller.\n",
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