Geodesic
Composite positive integers whose sum of prime factors is prime
Archivum mathematicum, Tome 56 (2020) no. 1, pp. 49-64

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In this note, we show that the counting function of the number of composite positive integers $n\le x$ such that $\beta (n)=\sum _{p\mid n} p$ is a prime is of order of magnitude at least $x/(\log x)^3$ and at most $x/ \log x$.
In this note, we show that the counting function of the number of composite positive integers $n\le x$ such that $\beta (n)=\sum _{p\mid n} p$ is a prime is of order of magnitude at least $x/(\log x)^3$ and at most $x/ \log x$.
DOI : 10.5817/AM2020-1-49
Classification : 11N25, 11N36
Keywords: primes; applications of sieve methods 
Luca, Florian; Moodley, Damon. Composite positive integers whose sum of prime factors is prime. Archivum mathematicum, Tome 56 (2020) no. 1, pp. 49-64. doi: 10.5817/AM2020-1-49
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