On the average of the sum-of-\(p\)-prime-divisors function (Q2773339)
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scientific article; zbMATH DE number 1709930
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the average of the sum-of-\(p\)-prime-divisors function |
scientific article; zbMATH DE number 1709930 |
Statements
21 February 2002
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sum of divisor function
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Omega estimate
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On the average of the sum-of-\(p\)-prime-divisors function (English)
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Denote by \(\sigma_{(p)}(n)\) the sum of the divisors of \(n\) which are relatively coprime to \(p\). In the present paper it is shown that NEWLINE\[NEWLINE\sum_{n\leq x}\sigma_{(p)}(n)-{\pi^2x^2\over 12}\left(1-{1\over p}\right)=\Omega_{\pm}(x\log\log x).NEWLINE\]NEWLINE For the proof of this interesting result the authors use ideas of \textit{P. Erdős} and \textit{H. N. Shapiro} [Can. J. Math. 3, 375--385 (1951; Zbl 0044.03903)] and \textit{Y.-F. S. Pétermann} [J. Number Theory 30, 71--85 (1988; Zbl 0649.10034)].
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