因子和幂，极小性结果

摘要：

令$a > 1$。然后对某个正整数$n$求$a^n < n!$。我们表明，最小的这样的$n$是一对的可能性，或者是一种可能性，我们展示了如何计算。有三个有趣的数字序列在我们的论证中起着核心作用。本文是在Robbins \cite{Robbins}对Sterling因子近似的改进和\cite{Radford}的结果的基础上进行的

英文摘要：

Let $a > 1$. Then $a^n < n!$ for some positive integer $n$. We show that the smallest such $n$ is one of a pair of possibilities, or is one possibility, which we show how to calculate. There are three interesting numerical sequences which play a central role in our arguments. This paper is based on the improvement on Sterling's approximation of factorials due to Robbins \cite{Robbins} and results of \cite{Radford}

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