<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In the article we formalize some properties needed to prove that sequences of prime reciprocals are divergent. The aim is to show that the series exhibits log-log growth. We introduce some auxiliary notions as harmonic numbers, telescoping series, and prove some standard properties of logarithms and exponents absent in the Mizar Mathematical Library. At the end we proceed with square-free and square-containing parts of a natural number and reciprocals of corresponding products.</p></abstract>

In the article we formalize some properties needed to prove that sequences of prime reciprocals are divergent. The aim is to show that the series exhibits log-log growth. We introduce some auxiliary notions as harmonic numbers, telescoping series, and prove some standard properties of logarithms and exponents absent in the Mizar Mathematical Library. At the end we proceed with square-free and square-containing parts of a natural number and reciprocals of corresponding products.

Sequences of Prime Reciprocals. Preliminaries

Formalized Mathematics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Sequences of Prime Reciprocals. Preliminaries"}

In the article we formalize some properties needed to prove that sequences of prime reciprocals are divergent. The aim is to show that the series exhibits...

Sequences of Prime Reciprocals. Preliminaries

Published Online: Jul 28, 2018

Page range: 69 - 79

Received: Mar 27, 2018

DOI: https://doi.org/10.2478/forma-2018-0006

Keywords
prime factorization, sequence of prime reciprocals, harmonic number

© 2018 Adam Grabowski, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Sequences of Prime Reciprocals. Preliminaries

Published Online: Jul 28, 2018

Page range: 69 - 79

Received: Mar 27, 2018

DOI: https://doi.org/10.2478/forma-2018-0006

Keywordsprime factorization, sequence of prime reciprocals, harmonic number

© 2018 Adam Grabowski, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
prime factorization, sequence of prime reciprocals, harmonic number