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Jul 1, 2020 at 3:18 comment added Sebastien Palcoux That’s right! One way for Question 2 (or weaker version 1) to survive would be to exclude the multiple of odd abundant numbers. The least odd number of abundancy index greater than $3$ is $1018976683725$.
Jul 1, 2020 at 1:56 history answered S. Carnahan CC BY-SA 4.0