论文标题
关于半数的计数函数
On the counting function of semiprimes
论文作者
论文摘要
半弹药是一个自然数字，可以写为两个素数的产物。研究了功能的渐近行为$π_2（x）$，半少数小于或等于$ x $的渐近行为。使用组合参数，确定$π_2（x）$的渐近系列，并明确给出所有术语。提出了用于计算渐近系列常数的算法，并将常数计算为20个重要数字。研究了渐近系列的部分总和的误差。还提出了这种方法对$ k $ primes的产品的概括，也提出了$ k \ geq 3 $的概括。
A semiprime is a natural number which can be written as the product of two primes. The asymptotic behaviour of the function $π_2(x)$, the number of semiprimes less than or equal to $x$, is studied. Using a combinatorial argument, asymptotic series of $π_2(x)$ is determined, with all the terms explicitly given. An algorithm for the calculation of the constants involved in the asymptotic series is presented and the constants are computed to 20 significant digits. The errors of the partial sums of the asymptotic series are investigated. A generalization of this approach to products of $k$ primes, for $k\geq 3$, is also proposed.
