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  "body": "\n## Definition\n\nA positive integer $n$ is perfect if it is equal to the sum of its positive divisors other than $n$.\nEquivalently, $\\sigma(n) = 2n$, where $\\sigma$ is the [[sum of divisors|009QCP5T3Z]].\n\n## Remarks\n\nThe first perfect numbers are $6$, $28$, $496$ and $8128$. For example, $28 = 1 + 2 + 4 + 7 + 14$.\nThe [[Euclid–Euler theorem|0WETJCKNRG]] describes all even perfect numbers by [[Mersenne primes|06GPJF9V7M]].\nNo odd perfect number is known, and it is an open problem whether one exists.\n\n## Explanations\n\n### L1 human\n\nA perfect number is the sum of its smaller divisors.\nThe divisors of $6$ other than $6$ are $1$, $2$ and $3$, and $1 + 2 + 3 = 6$.\n",
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