Abstract
Given an integer \(\mu\), we study the numbers n that satisfy the condition \(\frac{\mu}{n} + \sum_ {p \mid n} \frac {1} {p} \in \mathbb{N}\). This condition, which is reminiscent of the one satisfied by Giuga numbers (\(\mu=-1\)), also includes the so-called weak primary pseudoperfect numbers (\(\mu=1\)), see [9]. As a tribute to our late colleague Jonathan Sondow (1943–2020), we have named these numbers \(\mu \)-Sondow numbers. In this paper, we give several different characterizations of these numbers, all of them suggested by well-known characterizations of the Giuga numbers. We also relate these numbers to the well-known Erdős–Moser equation and we present some conjectures about them.
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Acknowledgement
The authors wish to thank Pieter Moree for his useful comments and suggestions, that helped us to improve the paper.
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Daniel Sadornil is partially supported by the Spanish Government under Project PID2019-110633GB-I00 from MCIN/AEI/10.13039/501100011033.
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Grau, J.M., Oller-Marcén, A.M. & Sadornil, D. On \(\mu\)-Sondow numbers. Acta Math. Hungar. 168, 217–227 (2022). https://doi.org/10.1007/s10474-022-01271-w
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DOI: https://doi.org/10.1007/s10474-022-01271-w