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

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
The sum of reduced harmonic series generated by any number of positive integer factors
Original language description
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.
Czech name
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Czech description
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Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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