On sequences of numbers not divisible one by another. (Q2611590)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On sequences of numbers not divisible one by another. |
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On sequences of numbers not divisible one by another. (English)
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1935
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Es sei \(a_1, a_2, \ldots\) eine wachsende Folge positiver ganzer Zahlen, so daß für i\( \neq j \) \(a_i\) kein Teiler von \(a_j\) ist. Es wird bewiesen \[ \sum_{a_i \leqq x} \frac{1}{a_i} = O \{ \log \, x \, (\log \, \log \, x)^ {- \frac{1}{2}} \}. \] Hieraus folgt, wenn \(N(x)\) die Anzahl der \(a_i \leqq x\) bezeichnet: \[ {\underset{x \to \infty} {\text{lim inf}}} \, \frac{N(x)}{x} = 0. \]
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