{"title":"以x/3为底的素数计数函数","authors":"I. Nuñez","doi":"10.12988/IMF.2021.912244","DOIUrl":null,"url":null,"abstract":"In this study, we present the function H(x)p based on Pk(x, a) introduced by Lehmer. H(x)p denotes the number of numbers that are not divisible by prime numbers < p but are divisible by p. Herein, we show that H(x)p can be obtained only using x 3 . We also present our own prime counting function based on H(x)p, that is, x 3 . Mathematics Subject Classification: 11A41, 11N05","PeriodicalId":107214,"journal":{"name":"International Mathematical Forum","volume":"42 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Prime counting function in base of x/3\",\"authors\":\"I. Nuñez\",\"doi\":\"10.12988/IMF.2021.912244\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this study, we present the function H(x)p based on Pk(x, a) introduced by Lehmer. H(x)p denotes the number of numbers that are not divisible by prime numbers < p but are divisible by p. Herein, we show that H(x)p can be obtained only using x 3 . We also present our own prime counting function based on H(x)p, that is, x 3 . Mathematics Subject Classification: 11A41, 11N05\",\"PeriodicalId\":107214,\"journal\":{\"name\":\"International Mathematical Forum\",\"volume\":\"42 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1900-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Mathematical Forum\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.12988/IMF.2021.912244\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Mathematical Forum","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.12988/IMF.2021.912244","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
In this study, we present the function H(x)p based on Pk(x, a) introduced by Lehmer. H(x)p denotes the number of numbers that are not divisible by prime numbers < p but are divisible by p. Herein, we show that H(x)p can be obtained only using x 3 . We also present our own prime counting function based on H(x)p, that is, x 3 . Mathematics Subject Classification: 11A41, 11N05
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