|
A simple proof of generalizations of number-theoretic sums |
|---|---|
| รหัสดีโอไอ | |
| Creator | 1. Yanapat Tongron 2. Narakorn Rompurk Kanasri |
| Title | A simple proof of generalizations of number-theoretic sums |
| Publisher | Research and Development Office, Prince of Songkla University |
| Publication Year | 2565 |
| Journal Title | Songklanakarin Journal of Science an Technology (SJST) |
| Journal Vol. | 44 |
| Journal No. | 2 |
| Page no. | 450-458 |
| Keyword | arithmetic function, Eulerโs phi-function, Mรถbius function, Mรถbius inversion formula |
| URL Website | https://rdo.psu.ac.th/sjst/index.php |
| ISSN | 0125-3395 |
| Abstract | For positive integers ๐', ๐', and ๐', let ๐'๐'๐'(๐') be the sum of all elements in the finite set {๐'ฅ๐': 1 โค ๐'ฅ โค ๐'โ๐' , (๐'ฅ, ๐') = 1}.The formula for ๐'๐'๐'(๐') is established and simpler formulae for ๐'๐'๐'(๐') under some conditions on ๐' and ๐' are verified. The explicitformulae for ๐'12๐'(๐') and ๐'22๐'(๐'), where 2๐'|๐' and ๐' โฅ 1, are also provided |
