Moments of the shifted prime divisor function

Mikhail R. Gabdullin

Let $ω^*(n) = \{d|n: d=p-1, \mbox{$p$ is a prime}\}$. We show that, for each integer $k\ge 2$, $$\sum _{n\le x}{\omega }^{\ast }(n{)}^k\asymp x(\log x{)}^{2^k-k-1},$$ where the implied constant m…