Research notes on a density problem of Erdős (Q1587828)
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scientific article; zbMATH DE number 1538458
| Language | Label | Description | Also known as |
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| English | Research notes on a density problem of Erdős |
scientific article; zbMATH DE number 1538458 |
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Research notes on a density problem of Erdős (English)
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28 February 2001
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If \(P(n)\) denotes the largest prime factor of \(n\), the author evaluates the cardinality \(S(x)\) of the set of integers \(n\) not more than \(x\) and that do not divide \(P(n)!\), a problem proposed by \textit{P. Erdős} in [Am. Math. Mon. 98, 965 (1991)]. The author proves elegantly that \(S(x)/x\ll\exp(-0.25\sqrt{\log x})\), improving an earlier estimate of \textit{I. Kastanas} [Am. Math. Mon. 101, 179 (1994)].
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primes
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factorial
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largest prime factor
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density
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