Two Calculation Methods of the Sum of Reciprocals of All Products Generated by Prime Factors of the Number 2022
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F60162694%3AG43__%2F24%3A00560611" target="_blank" >RIV/60162694:G43__/24:00560611 - isvavai.cz</a>
Result on the web
<a href="https://mitav.unob.cz/data/Mitav2023.pdf" target="_blank" >https://mitav.unob.cz/data/Mitav2023.pdf</a>
DOI - Digital Object Identifier
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Alternative languages
Result language
angličtina
Original language name
Two Calculation Methods of the Sum of Reciprocals of All Products Generated by Prime Factors of the Number 2022
Original language description
This paper is inspired by one task on the sum of a special infinite series on the Berkeley Math Circle. The task was to determine the sum of all the unit fractions that have denominators with only factors consisting of all prime divisors of the number 2002, i.e. the primes 2, 7, 11, 13. We updated this task to determine the sum of reciprocals of all products generated by all prime divisors of the number 2022. This series can be consider as the reduced harmonic series generated by three primes 2, 3, 337. The sum of this series was calculated analytically by two methods and also numerically by using the programming language of the computer algebra system Maple 2022. By these three attempts we obtained the same result. Finally, we generalized the obtained result and presented a formula for the sum of these series with n generating positive integers different from 1.
Czech name
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Czech description
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Classification
Type
D - Article in proceedings
CEP classification
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OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
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Continuities
V - Vyzkumna aktivita podporovana z jinych verejnych zdroju
Others
Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
MITAV 2023
ISBN
978-80-7582-290-1
ISSN
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e-ISSN
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Number of pages
10
Pages from-to
60-69
Publisher name
Fakulta elektrotechniky a komunikačních technologií Vysokého učení technického v Brně
Place of publication
Brno
Event location
Brno
Event date
Jun 15, 2023
Type of event by nationality
EUR - Evropská akce
UT code for WoS article
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