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Composite positive integers whose sum of prime factors is prime

Florian Luca; Damon Moodley — 2020

Archivum Mathematicum

In this note, we show that the counting function of the number of composite positive integers $n \leq x$ such that $β (n) = \sum_{p ∣ n} p$ is a prime is of order of magnitude at least $x / {(log x)}^{3}$ and at most $x / log x$ .

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