{"title":"取决于函数 φ(n)、ψ(n) 和 σ(n) 的表达式的下界","authors":"Stoyan Dimitrov","doi":"10.7546/nntdm.2023.29.4.713-716","DOIUrl":null,"url":null,"abstract":"The inequalities \\varphi^2(n)+\\psi^2(n)+\\sigma^2(n) \\geq 3n^2+2n+3 , \\varphi(n)\\psi(n)+\\varphi(n)\\sigma(n)+\\sigma(n)\\psi(n) \\geq 3n^2+2n-1 connecting \\varphi(n), \\psi(n) and \\sigma(n)-functions are formulated and proved.","PeriodicalId":44060,"journal":{"name":"Notes on Number Theory and Discrete Mathematics","volume":"11 1","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2023-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Lower bounds on expressions dependent on functions φ(n), ψ(n) and σ(n)\",\"authors\":\"Stoyan Dimitrov\",\"doi\":\"10.7546/nntdm.2023.29.4.713-716\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The inequalities \\\\varphi^2(n)+\\\\psi^2(n)+\\\\sigma^2(n) \\\\geq 3n^2+2n+3 , \\\\varphi(n)\\\\psi(n)+\\\\varphi(n)\\\\sigma(n)+\\\\sigma(n)\\\\psi(n) \\\\geq 3n^2+2n-1 connecting \\\\varphi(n), \\\\psi(n) and \\\\sigma(n)-functions are formulated and proved.\",\"PeriodicalId\":44060,\"journal\":{\"name\":\"Notes on Number Theory and Discrete Mathematics\",\"volume\":\"11 1\",\"pages\":\"\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2023-11-21\",\"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.2023.29.4.713-716\",\"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.2023.29.4.713-716","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
Lower bounds on expressions dependent on functions φ(n), ψ(n) and σ(n)
The inequalities \varphi^2(n)+\psi^2(n)+\sigma^2(n) \geq 3n^2+2n+3 , \varphi(n)\psi(n)+\varphi(n)\sigma(n)+\sigma(n)\psi(n) \geq 3n^2+2n-1 connecting \varphi(n), \psi(n) and \sigma(n)-functions are formulated and proved.
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