Superabundant Numbers and the Riemann Hypothesis

@article{Akbary2009SuperabundantNA,
  title={Superabundant Numbers and the Riemann Hypothesis},
  author={Amir Akbary and Zachary Friggstad},
  journal={The American Mathematical Monthly},
  year={2009},
  volume={116},
  pages={273-275}
}
For a lively exposition of this theorem and its connection to the Riemann Hypothesis see [5]. In this note, we propose a method that will establish explicit upper bounds for σ(n)/en log log n. Our main observation is that the least number violating the inequality (2) should be a superabundant number. A positive integer n is said to be superabundant if σ(m)/m < σ(n)/n for all m < n. The first 20 superabundant numbers are 1, 2, 4, 6, 12, 24, 36, 48, 60, 120, 180, 240, 360, 720, 840, 1260, 1680… CONTINUE READING

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