{"title":"固有因子的无幂和","authors":"P. Pollack, A. Roy","doi":"10.4064/cm8616-10-2021","DOIUrl":null,"url":null,"abstract":". Let s ( n ) := (cid:80) d | n,d<n d denote the sum of the proper divisors of n . It is natural to conjecture that for each integer k ≥ 2 , the equivalence n is k th powerfree ⇐⇒ s ( n ) is k th powerfree holds almost always (meaning, on a set of asymptotic density 1 ). We prove this for k ≥ 4 .","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Powerfree sums of proper divisors\",\"authors\":\"P. Pollack, A. Roy\",\"doi\":\"10.4064/cm8616-10-2021\",\"DOIUrl\":null,\"url\":null,\"abstract\":\". Let s ( n ) := (cid:80) d | n,d<n d denote the sum of the proper divisors of n . It is natural to conjecture that for each integer k ≥ 2 , the equivalence n is k th powerfree ⇐⇒ s ( n ) is k th powerfree holds almost always (meaning, on a set of asymptotic density 1 ). We prove this for k ≥ 4 .\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2021-06-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4064/cm8616-10-2021\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4064/cm8616-10-2021","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
摘要
． 让s (n) = (cid): 80) d | n, d < n d合适divisors》denote the sum of n。自然是每到conjecture that for《equivalence n是整数k≥2,k th powerfree⇐⇒s (n)是k th powerfree珍藏几乎总是(asymptotic密度之意义,on a组1)。我们证明这个for k≥4。
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