On the function \(a_ p\), \(p^{a_ p(n)}\| n\), \((n>1)\). (English) Zbl 0798.11003

Verf. untersucht arithmetische Eigenschaften der Ordnungsfunktionen \(a_ p\) \((p \in \mathbb P)\), \(\mathbb P\) die Menge aller Primzahlen; sie sind als additive Funktionen durch \(a_ p (q^ k) = k\) falls \(q=p\), 0 falls \(q \neq p\) definiert. Er bestimmt die Konvergenzabszisse der erzeugenden Dirichlet- Reihe \((\sigma = 1)\), den Mittelwert von \(a_ p( = 1/(p-1))\) sowie die natürlichen Dichten der Niveaumengen \(a_ p^{-1} (\{k\})\) und \(\{n:a_ p(n) | n\}\). Die Beweise sind elementar.


11A25 Arithmetic functions; related numbers; inversion formulas
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