关于互质部分的因子分解
On factorizations into coprime parts
摘要：
令$f(n)$和$g(n)$是将$n$分解为大于1的整数的无序和有序因式分解的数目。令$F(n)$和$G(n)$具有因子互质的附加限制。对所有实数$β$，我们建立了$F(n)^β$和$G(n)^β$直到$x$的和的渐近界;对所有负数$β$，我们建立了$f(n)^β$和$g(n)^β$的渐近界.
英文摘要：
Let $f(n)$ and $g(n)$ be the number of unordered and ordered factorizations of $n$ into integers larger than one. Let $F(n)$ and $G(n)$ have the additional restriction that the factors are coprime. We establish the asymptotic bounds for the sums of $F(n)^β$ and $G(n)^β$ up to $x$ for all real $β$ and the asymptotic bounds for $f(n)^β$ and $g(n)^β$ for all negative $β$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
