论文标题
关于非缺陷数字的小质量因素
On the small prime factors of a non-deficient number
论文作者
论文摘要
令$σ（n）$成为$ n $的正分离的总和。如果$σ（n）\ geq 2n $，一个数字是非缺陷的。我们为奇数非缺陷数量的不同主要因素的数量建立了新的下限，其第二小，第三小和第四最小的素数因素。我们还获得了奇数完美数字的更紧密的界限。我们还讨论了$σ（n！+1）$，$σ（2^n+1）$和相关序列的行为。
Let $σ(n)$ to be the sum of the positive divisors of $n$. A number is non-deficient if $σ(n) \geq 2n$. We establish new lower bounds for the number of distinct prime factors of an odd non-deficient number in terms of its second smallest, third smallest and fourth smallest prime factors. We also obtain tighter bounds for odd perfect numbers. We also discuss the behavior of $σ(n!+1)$, $σ(2^n+1)$, and related sequences.
