On cycles in the sequence of unitary Cayley graphs
The authors prove the following results. (1) Given \(r\in N\), there is \(N(r)\in N\), depending only on \(r\), such that \(p_k(n)=0\) for all \(k\geq N(r)\) and for all \(n\) with at most \(r\) different prime divisors. (2) For every \(r\) there are non-trivial arithmetic functions \(f\) satisfying the following two properties: (i) \(f\) is a \(Z\)-linear combination of multiplicative arithmetic functions, and (ii) \(f(n)=0\) for every \(n\) with at most \(r\) different prime divisors.
scientific article; zbMATH DE number 2083700
scientific article