On a density problem of Erdös
For a positive integer n, let P(n) denotes the largest prime divisor of n and define the set: 𝒮(x)=𝒮={n≤x:n does not divide P(n)!}. Paul Erdös has proposed that |S|=o(x) as x→∞, where |S| is the number of n∈S. This was proved by Ilias Kastanas. In this paper we will show the stronger result that...
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| Format: | Article |
| Language: | English |
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Wiley
1999-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171299226555 |
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| _version_ | 1832564069252464640 |
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| author | Safwan Akbik |
| author_facet | Safwan Akbik |
| author_sort | Safwan Akbik |
| collection | DOAJ |
| description | For a positive integer n, let P(n) denotes the largest prime divisor of n and define the set: 𝒮(x)=𝒮={n≤x:n does not divide P(n)!}. Paul Erdös has proposed that |S|=o(x) as x→∞, where |S| is the number of n∈S. This was proved by Ilias Kastanas. In this paper we will show the stronger result that |S|=O(xe−1/4logx). |
| format | Article |
| id | doaj-art-96dfdb8fe92d4a108235b50caf803b08 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1999-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-96dfdb8fe92d4a108235b50caf803b082025-02-03T01:11:49ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251999-01-0122365565810.1155/S0161171299226555On a density problem of ErdösSafwan Akbik0Department of Mathematics, Hofstra University, Hempstead 11550, NY, USAFor a positive integer n, let P(n) denotes the largest prime divisor of n and define the set: 𝒮(x)=𝒮={n≤x:n does not divide P(n)!}. Paul Erdös has proposed that |S|=o(x) as x→∞, where |S| is the number of n∈S. This was proved by Ilias Kastanas. In this paper we will show the stronger result that |S|=O(xe−1/4logx).http://dx.doi.org/10.1155/S0161171299226555Number theoryprimesfactorialdensitydivisibility. |
| spellingShingle | Safwan Akbik On a density problem of Erdös International Journal of Mathematics and Mathematical Sciences Number theory primes factorial density divisibility. |
| title | On a density problem of Erdös |
| title_full | On a density problem of Erdös |
| title_fullStr | On a density problem of Erdös |
| title_full_unstemmed | On a density problem of Erdös |
| title_short | On a density problem of Erdös |
| title_sort | on a density problem of erdos |
| topic | Number theory primes factorial density divisibility. |
| url | http://dx.doi.org/10.1155/S0161171299226555 |
| work_keys_str_mv | AT safwanakbik onadensityproblemoferdos |