论文标题
关于R. M. Murty和V. K. Murty的猜想
On a conjecture of R. M. Murty and V. K. Murty
论文作者
论文摘要
令$ω^*（n）$为Primes $ p $的数量，以便$ p-1 $划分$ n $。最近，R。M。Murty和V. K. Murty证明了$$ x（\ log \ log x）^3 \ ll \ sum_ {n \ le x}ω^*（n）^2 \ ll x \ log x。 x $$ as $ x \ rightarrow \ infty $。在此简短说明中，我们通过显示$$ \ sum_ {n \ le x}ω^*（n）^2 \ asymp x \ logx。$$给出了正确的总和。
Let $ω^*(n)$ be the number of primes $p$ such that $p-1$ divides $n$. Recently, R. M. Murty and V. K. Murty proved that $$x(\log\log x)^3\ll\sum_{n\le x}ω^*(n)^2\ll x\log x.$$ They further conjectured that there is some positive constant $C$ such that $$\sum_{n\le x}ω^*(n)^2\sim Cx\log x$$ as $x\rightarrow \infty$. In this short note, we give the correct order of the sum by showing that $$\sum_{n\le x}ω^*(n)^2\asymp x\log x.$$
