Geodesic
On a multiplicative function on the set of shifted primes
Matematičeskie zametki, Tome 64 (1998) no. 3, pp. 457-464

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It is proved that if $f(n)$ is a multiplicative function taking a value $\xi$ on the set of primes such that $\xi^3=1$, $\xi\ne1$ and $f^3(p^r)=1$ for $r\ge2$, then there exists $\theta\in(0,1)$, for which $$ \biggl|\sum_{p\le x}f(p+1)\biggr|\le\theta\pi(x), $$ where $$ \pi(x)=\sum_{p\le x}1. $$ 
@article{MZM_1998_64_3_a14,
     author = {M. B. Khripunova},
     title = {On a multiplicative function on the set of shifted primes},
     journal = {Matemati\v{c}eskie zametki},
     pages = {457--464},
     publisher = {mathdoc},
     volume = {64},
     number = {3},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1998_64_3_a14/}
}
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M. B. Khripunova. On a multiplicative function on the set of shifted primes. Matematičeskie zametki, Tome 64 (1998) no. 3, pp. 457-464. http://geodesic.mathdoc.fr/item/MZM_1998_64_3_a14/