Multiplicative Bases and an Erdős Problem

Abstract

In this paper we investigate how small the density of a multiplicative basis of order h can be in {1,2,...,n} and in ℤ+. Furthermore, a related problem of Erdős is also studied: How dense can a set of integers be, if none of them divides the product of h others?

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Correspondence to Csaba Sándor.

Additional information

This author was supported by the Hungarian Scientific Research Funds (Grant Nr. OTKA PD115978 and OTKA K108947) and the János Bolyai Research Scholarship of the Hungarian Academy of Sciences.

This author was supported by the OTKA Grant No. K109789 and the János Bolyai Research Scholarship of the Hungarian Academy of Sciences.

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Pach, P.P., Sándor, C. Multiplicative Bases and an Erdős Problem. Combinatorica 38, 1175–1203 (2018). https://doi.org/10.1007/s00493-016-3588-2

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Mathematics Subject Classification (2000)

  • 11B05
  • 11B83