A perfect number is an integer $n$ greater than $1$ that equals the sum of its factors, excluding $n$ itself. For example, $6 = 1 + 2 +3 $ so $6$ is perfect. It is unknown whether there are any odd perfect numbers. My question is, are there any odd integers $n$ greater than $1$ such that the sum of all of $n$'s factors, excluding $n$, is greater than $n$? In number-theoretic language, does there exist odd $n$ with $\sigma(n) > 2n$?
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Look up "abundant numbers" in Wikipedia and at https://oeis.org/A005101