Two functions in number theory and some upper bounds for the Smarandache's function (Q2711377)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Two functions in number theory and some upper bounds for the Smarandache's function |
scientific article |
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23 June 2002
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greatest common divisor
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Euler function
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Smarandache function
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Two functions in number theory and some upper bounds for the Smarandache's function (English)
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The authors present some well-known properties of the Euler \(\varphi\)-function, investigate the functions \(\psi_1(n)=\sum_{i=1}^n \frac{n}{(i,n)}\), \(\psi_2(n)=\sum_{i=1}^n \frac{i}{(i,n)}\) and, as an application, obtain certain results for the so-called Smarandache function \(S(n)\), where \(S(n)\) is defined as the smallest positive integer \(k\) such that \(n\) divides \(k!\).
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