The sum of reduced harmonic series generated by any number of positive integer factors

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F60162694%3AG43__%2F23%3A00558143" target="_blank" >RIV/60162694:G43__/23:00558143 - isvavai.cz</a>

Výsledek na webu

<a href="http://doi.org/10.37394/232021.2022.2.18" target="_blank" >http://doi.org/10.37394/232021.2022.2.18</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.37394/232021.2022.2.18" target="_blank" >10.37394/232021.2022.2.18</a>

Jazyk výsledku

angličtina

Název v původním jazyce

The sum of reduced harmonic series generated by any number of positive integer factors

Popis výsledku v původním jazyce

This paper is a free continuation of the author’s previous papers dealing with the sums of the reduced harmonic series generated of reciprocals of all products generated by all prime divisors of the numbers 2002 and 2022, that were inspired by one task on the sum of a special infinite series on the Berkeley Math Circle. We determined the sums of these series, i.e. the series of all the unit fractions that have denominators with only factors consisting of all prime divisors of the numbers 2022 and 2002, analytically and also by calculation in computer algebra system Maple. In this paper, we generalize our considerations and derive two formulas that obviously hold not only to series generated by n prime numbers, but also to series generated by n positive integers.

Název v anglickém jazyce

The sum of reduced harmonic series generated by any number of positive integer factors

Popis výsledku anglicky

This paper is a free continuation of the author’s previous papers dealing with the sums of the reduced harmonic series generated of reciprocals of all products generated by all prime divisors of the numbers 2002 and 2022, that were inspired by one task on the sum of a special infinite series on the Berkeley Math Circle. We determined the sums of these series, i.e. the series of all the unit fractions that have denominators with only factors consisting of all prime divisors of the numbers 2022 and 2002, analytically and also by calculation in computer algebra system Maple. In this paper, we generalize our considerations and derive two formulas that obviously hold not only to series generated by n prime numbers, but also to series generated by n positive integers.

Druh

J_ost - Ostatní články v recenzovaných periodicích

CEP obor

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OECD FORD obor

10101 - Pure mathematics

Projekt

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Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2022

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

WSEAS Transactions on Equations

ISSN

2944-9146

e-ISSN

2732-9976

Svazek periodika

2

Číslo periodika v rámci svazku

7/2022

Stát vydavatele periodika

GR - Řecká republika

Počet stran výsledku

11

Strana od-do

112-122

Kód UT WoS článku

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EID výsledku v databázi Scopus

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