Consecutive integers with close kernels

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17310%2F19%3AA200240Q" target="_blank" >RIV/61988987:17310/19:A200240Q - isvavai.cz</a>
Result on the web
<a href="https://www.cambridge.org/core/journals/canadian-mathematical-bulletin/article/consecutive-integers-with-close-kernels/95143DE6D827240FAF167677B6205C6C" target="_blank" >https://www.cambridge.org/core/journals/canadian-mathematical-bulletin/article/consecutive-integers-with-close-kernels/95143DE6D827240FAF167677B6205C6C</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4153/S0008439518000085" target="_blank" >10.4153/S0008439518000085</a>

Result language
angličtina
Original language name
Consecutive integers with close kernels
Original language description
Let k be an arbitrary positive integer and let gamma(n) stand for the product of the distinct prime factors of n. For each integer n >= 2, let a(n) and b(n) stand respectively for the maximum and the minimum of the k integers gamma(n + 1), gamma(n + 2), ..., gamma(n + k). We show that lim inf(n ->infinity) a(n)/b(n) = 1. We also prove that the same result holds in the case of the Euler function and the sum of the divisors function, as well as the functions omega(n) and Omega(n), which stand respectively for the number of distinct prime factors of n and the total number of prime factors of n counting their multiplicity.
Czech name
—
Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA17-02804S" target="_blank" >GA17-02804S: Properties of number sequences and their applications</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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