Abstract
LetM ⊂ ℕ be a multiplicative set with 1∈M andmn∈M if and only ifm∈M,n∈M for (m,n)=1. It is shown by elementary means that there exists the asymptotic density of the setM∩(M−1) for every multiplicative setM. The density is positive if and only ifM possesses a positive density and 2ν∈M for some ν∈ℕ. This result is slightly generalized to sums over multiplicative functionsf with |f|≤1.
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Lucht, L., Tuttas, F. Aufeinanderfolgende Elemente in multiplikativen Zahlenmengen. Monatshefte für Mathematik 87, 15–19 (1979). https://doi.org/10.1007/BF01470935
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DOI: https://doi.org/10.1007/BF01470935