论文标题
Mertens的主要产品配方，解剖
Mertens' prime product formula, dissected
论文作者
论文摘要
1874年，梅尔滕斯（Mertens）在所有Primes $ p $ the $ p $ to $ x $上闻名为产品$ p/p/p/p/p/par。另一方面，一个人可能会将梅尔滕斯的主要产品扩展到数字$ n $的系列中，而只有很小的主要因素。将这样的系列限制在数字$ n $的情况下是很自然的，其中固定的数字$ k $是主要因素。在本文中，我们为每个$ k $获得这些系列的公式，共同剖析了梅尔滕斯的原始估计。证明是通过组合风味的基本方法。
In 1874, Mertens famously proved an asymptotic formula for the product $p/(p-1)$ over all primes $p$ up to $x$. On the other hand, one may expand Mertens' prime product into series over numbers $n$ with only small prime factors. It is natural to restrict such series to numbers $n$ with a fixed number $k$ of prime factors. In this article, we obtain formulae for these series for each $k$, which together dissect Mertens' original estimate. The proof is by elementary methods of a combinatorial flavor.
