论文标题
关于满足罗宾不平等的数字，下一个反例的属性和改进的特定界限
On numbers satisfying Robin's inequality, properties of the next counterexample and improved specific bounds
论文作者
论文摘要
定义$ s（n）：= n^{ - 1}σ（n）$（$σ（n）：= \ sum_ {d | n} d）$ and $ω（n）$是$ n $的prime级数。 $ s $的属性之一起着中心作用：$ s（p^a）> s（q^b）$如果$ p <q $是质数，则在$ a，b $ a，b $ a，b \ geqslant 1 $外没有特殊条件。该结果与多样性置换定理相结合，将帮助我们建立下一个反例（例如$ c $）的Robin的不等式$ s（n）<e^γ\ log \ log \ log \ log n $的属性。数字$ c $是超级繁殖的，$ω（c）$必须大于接近10亿的数字。另外，比率$ p_ {ω（c）} / \ log c $具有下限和上限。最多$ω（C）/14 $多重参数大于$ 1 $。最后但并非最不重要的一点是，我们将简单的方法应用于各种数字类别的不平等现象。
Define $s (n) := n^{- 1} σ(n)$ ($σ(n):=\sum_{d|n}d )$ and $ω(n)$ is the number of prime divisors of $n$. One of the properties of $s$ plays a central role: $s (p^a) > s (q^b)$ if $p < q$ are prime numbers, with no special condition on $a, b$ other than $a, b \geqslant 1$. This result, combined with the Multiplicity Permutation theorem, will help us establish properties of the next counterexample (say $c$) to Robin's inequality $s (n) < e^γ \log \log n$. The number $c$ is superabundant, and $ω(c)$ must be greater than a number close to one billion. In addition, the ratio $p_{ω(c)} / \log c$ has a lower and upper bound. At most $ω(c)/14$ multiplicity parameters are greater than $1$. Last but not least, we apply simple methods to sharpen Robin's inequality for various categories of numbers.
