{"title":"在某些有理数完全数上","authors":"J. Sándor","doi":"10.7546/nntdm.2022.28.3.525-532","DOIUrl":null,"url":null,"abstract":"We continue the study from [1], by studying equations of type $\\psi(n) = \\dfrac{k+1}{k} \\cdot \\ n+a,$ $a\\in \\{0, 1, 2, 3\\},$ and $\\varphi(n) = \\dfrac{k-1}{k} \\cdot \\ n-a,$ $a\\in \\{0, 1, 2, 3\\}$ for $k > 1,$ where $\\psi(n)$ and $\\varphi(n)$ denote the Dedekind, respectively Euler's, arithmetical functions.","PeriodicalId":44060,"journal":{"name":"Notes on Number Theory and Discrete Mathematics","volume":" ","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2022-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On certain rational perfect numbers, II\",\"authors\":\"J. Sándor\",\"doi\":\"10.7546/nntdm.2022.28.3.525-532\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We continue the study from [1], by studying equations of type $\\\\psi(n) = \\\\dfrac{k+1}{k} \\\\cdot \\\\ n+a,$ $a\\\\in \\\\{0, 1, 2, 3\\\\},$ and $\\\\varphi(n) = \\\\dfrac{k-1}{k} \\\\cdot \\\\ n-a,$ $a\\\\in \\\\{0, 1, 2, 3\\\\}$ for $k > 1,$ where $\\\\psi(n)$ and $\\\\varphi(n)$ denote the Dedekind, respectively Euler's, arithmetical functions.\",\"PeriodicalId\":44060,\"journal\":{\"name\":\"Notes on Number Theory and Discrete Mathematics\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2022-08-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Notes on Number Theory and Discrete Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.7546/nntdm.2022.28.3.525-532\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Notes on Number Theory and Discrete Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.7546/nntdm.2022.28.3.525-532","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
We continue the study from [1], by studying equations of type $\psi(n) = \dfrac{k+1}{k} \cdot \ n+a,$ $a\in \{0, 1, 2, 3\},$ and $\varphi(n) = \dfrac{k-1}{k} \cdot \ n-a,$ $a\in \{0, 1, 2, 3\}$ for $k > 1,$ where $\psi(n)$ and $\varphi(n)$ denote the Dedekind, respectively Euler's, arithmetical functions.
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