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https://open.uns.ac.rs/handle/123456789/18128
Title: | On quotients of values of Euler's function on the Catalan numbers | Authors: | Bašić Bojan | Issue Date: | 2016 | Journal: | Journal of Number Theory | Abstract: | © 2016 Elsevier Inc. In a recent work, Luca and Stănică examined quotients of the form φ(Cm)φ(Cn), where φ is Euler's totient function and C0,C1,C2… is the sequence of the Catalan numbers. They observed that the number 4 (and analogously 14) appears noticeably often as a value of these quotients. We give an explanation of this phenomenon, based on Dickson's conjecture. It turns out not only that the value 4 is (in a certain sense) special in relation to the quotients φ(Cn+1)φ(Cn), but also that the value 4k has similar “special” properties with respect to the quotients φ(Cn+k)φ(Cn), and in particular we show that Dickson's conjecture implies that, for each k, the number 4k appears infinitely often as a value of the quotients φ(Cn+k)φ(Cn). | URI: | https://open.uns.ac.rs/handle/123456789/18128 | ISSN: | 0022-314X | DOI: | 10.1016/j.jnt.2016.05.023 |
Appears in Collections: | PMF Publikacije/Publications |
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