The least common multiple of random sets of positive integers

Javier Cilleruelo; Juanjo Rué; Paulius Šarka; Ana Zumalacárregui

The least common multiple of random sets of positive integers

Number Theory 2013-12-16 v2

Authors: Javier Cilleruelo , Juanjo Rué , Paulius Šarka , Ana Zumalacárregui

Abstract

We study the typical behavior of the least common multiple of the elements of a random subset $A\subset \{1,\dots, n\}$ . For example we prove that $\text{lcm}\{a:\ a\in A\}=2^{n(1+o(1))}$ for almost all subsets $A\subset\{1,\dots,n\}$ .

Keywords

least common multiple random sets positive integers number theory probabilistic number theory

Cite

@article{arxiv.1112.3013,
  title  = {The least common multiple of random sets of positive integers},
  author = {Javier Cilleruelo and Juanjo Rué and Paulius Šarka and Ana Zumalacárregui},
  journal= {arXiv preprint arXiv:1112.3013},
  year   = {2013}
}

Comments

11 pages. The manuscript has been rearranged. New results were included and some of the proofs improved

The least common multiple of random sets of positive integers

Abstract

Keywords

Cite

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