Journal article
On the counting function of semiprimes
- Abstract:
- A semiprime is a natural number which can be written as the product of two primes. The asymptotic behaviour of the function $\pi_2(x)$, the number of semiprimes less than or equal to $x$, is studied. Using a combinatorial argument, asymptotic series of $\pi_2(x)$ is determined, with all the terms explicitly given. An algorithm for the calculation of the constants involved in the asymptotic series is presented and the constants are computed to 20 significant digits. The errors of the partial sums of the asymptotic series are investigated. A generalization of this approach to products of $k$ primes, for $k\geq 3$, is also proposed.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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(Preview, Version of record, pdf, 535.6KB, Terms of use)
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- Publication website:
- http://math.colgate.edu/~integers/vol21.html
Authors
- Publisher:
- Colgate University, Charles University and DIMATIA
- Journal:
- Integers More from this journal
- Volume:
- 21
- Article number:
- A122
- Publication date:
- 2021-12-13
- Acceptance date:
- 2021-12-07
- EISSN:
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1867-0660
- ISSN:
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1867-0652
- Language:
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English
- Keywords:
- Pubs id:
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1116231
- Local pid:
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pubs:1116231
- Deposit date:
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2021-11-09
- ARK identifier:
Terms of use
- Copyright holder:
- Crişan and Erban
- Copyright date:
- 2021
- Rights statement:
- All works of this journal are licensed under a Creative Commons Attribution 4.0 International License so that all content is freely available without charge to the users or their institutions. Users are allowed to read, download, copy, distribute, print, search, or link to the full texts of the articles in this journal without asking prior permission from the publisher or the author. This is in accordance with the BOAI definition of open access.
- Licence:
- CC Attribution (CC BY)
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