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Prime and Nonprime Totatives: A Sharp Construction and Exact Thresholds
For \(n\ge2\), let \(A(n)=π(n)-ω(n)\) and \(B(n)=ϕ(n)-π(n)+ω(n)\) denote the numbers of prime and nonprime totatives of \(n\), respectively, with \(1\) included in \(B(n)\). We construct an explicit injectively parametrized family \(\mathcal C_n\) of composite totatives by completing suitably restri
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