论文标题
在与整数b-Multiph的集合中链接到除数函数的乘法函数的总和5
On a sum of a multiplicative function linked to the divisor function over the set of integers B-multiple of 5
论文作者
论文摘要
令$ d（n）$和$ d^{\ ast}（n）$为除数的数量和整数$ n \ geq1 $的单一除数的数量。在本文中，我们证明了\ [\ inset {n \ in \ mathcal {b}}} {\ underSet {n \ leq x} {\ sum}}} \ frac {d（n）} ％tcimacro {\ u {b2}}％％beginexpansion {{{}^2}％％endexpansion} {123} {p} {p} {p} {\ prof} {\ prof}（1- \ frac {1} {{{}^2}％％endexpansion}+\ frac {1} {2p^{3}}）x+\ m nathcal {o} \ left（x^{\ frac {\ frac {\ ln8} {\ ln10} {\ ln10} x \ geqslant1，〜\ varepsilon> 0 \ right），\]，其中$ \ mathcal {b} $是包含任何不是$ 5的整数的集合
Let $d(n)$ and $d^{\ast}(n)$ be the numbers of divisors and the numbers of unitary divisors of the integer $n\geq1$. In this paper, we prove that \[ \underset{n\in\mathcal{B}}{\underset{n\leq x}{\sum}}\frac{d(n)}{d^{\ast}% (n)}=\frac{16π% %TCIMACRO{\U{b2}}% %BeginExpansion {{}^2}% %EndExpansion }{123}\underset{p}{\prod}(1-\frac{1}{2p% %TCIMACRO{\U{b2}}% %BeginExpansion {{}^2}% %EndExpansion }+\frac{1}{2p^{3}})x+\mathcal{O}\left( x^{\frac{\ln8}{\ln10}+\varepsilon }\right) ,~\left( x\geqslant1,~\varepsilon>0\right) , \] where $\mathcal{B}$ is the set which contains any integer that is not a multiple of $5,$ but some permutations of its digits is a multiple of $5.$
