On the Sums of Infinite and Finite Series of Reciprocals of Prime Factors and Divisors of the Number 2025

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F60162694%3AG43__%2F26%3A00566643" target="_blank" >RIV/60162694:G43__/26:00566643 - isvavai.cz</a>
Result on the web
<a href="https://mitav.unob.cz/data/235_FVT_ISBN_642-8_e-kniha.pdf" target="_blank" >https://mitav.unob.cz/data/235_FVT_ISBN_642-8_e-kniha.pdf</a>
DOI - Digital Object Identifier
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Result language
angličtina
Original language name
On the Sums of Infinite and Finite Series of Reciprocals of Prime Factors and Divisors of the Number 2025
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, that is the primes 2, 7, 11 and 13. We updated this task to determine the sum of reciprocals of all products generated by all prime divisors of the number 2025. This series can be consider as the reduced harmonic series generated by two primes 3 and 5. The sum of this series is calculated analytically and finally also numerically by using the programming language of the computer algebra system Maple. By these both attempts we obtained the same result. The paper also includes a relatively easy determination of the sum of the reciprocals of all positive divisors of the number 2025, i.e. the sum of the inverted values of numbers 1, 3, 5, 9, 15, 25, 27, 45, 75, 81, 135, 225, 405, 675 and 2025. Finally, generalizations of both results are presented.
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
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection
Mathematics, Information Technologies and Applied Sciences 2025 (post-conference proceedings of extended versions of selected papers)
ISBN
978-80-7582-642-8
ISSN
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e-ISSN
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Number of pages
10
Pages from-to
64-73
Publisher name
Univerzita obrany, Brno
Place of publication
Brno
Event location
Brno
Event date
Jun 19, 2025
Type of event by nationality
EUR - Evropská akce
UT code for WoS article
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