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arXiv · 1308.3678

Preventing Exceptions to Robins InEquality

Thomas Schwabhäuser
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Abstract

For sufficiently large n Ramanujan gave a sufficient condition for the truth Robin's InEquality $X(n):=\frac{σ(n)}{n\ln\ln n}<e^γ$ (RIE). The largest known violation of RIE is $n_8=5040$. In this paper Robin's multipliers are split into logarithmic terms $\mathcal{L}$ and relative divisor sums $\mathcal{G}$. A violation of RIE above $n_{8}$ is proposed to imply oscillations that cause $\mathcal{G}$ to exceed $\mathcal{L}$. To this aim Alaoglu and Erdős's conjecture for the CA numbers algorithm is used and the paper's key points are in section 4.2

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Thomas Schwabhäuser. 2013-08-26. Preventing Exceptions to Robins InEquality. https://arxiv.org/abs/1308.3678

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