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June 2012 Some arithmetic identities involving divisor functions
Şaban Alaca, Faruk Uygul, Kenneth S. Williams
Funct. Approx. Comment. Math. 46(2): 261-271 (June 2012). DOI: 10.7169/facm/2012.46.2.9

Abstract

For a positive integer $n$, let $\sigma(n):= \sum_{d \in \mathb{N}, d|n} d$. The explicit evaluation of such arithmetic sums as $\sum_{(a,b,c) \in \ABIFnn^3, a+2b+4c=n} \sigma(a)\sigma(b) \sigma(c)$ and $\sum_{(a,b) \in \ABIFnn^2, a+2b=n} a \sigma(a)\sigma(b)$ is carried out for all positive integers $n$.

Citation

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Şaban Alaca. Faruk Uygul. Kenneth S. Williams. "Some arithmetic identities involving divisor functions." Funct. Approx. Comment. Math. 46 (2) 261 - 271, June 2012. https://doi.org/10.7169/facm/2012.46.2.9

Information

Published: June 2012
First available in Project Euclid: 25 June 2012

zbMATH: 1318.11001
MathSciNet: MR2931670
Digital Object Identifier: 10.7169/facm/2012.46.2.9

Subjects:
Primary: 11A25
Secondary: 11F27

Rights: Copyright © 2012 Adam Mickiewicz University

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Vol.46 • No. 2 • June 2012
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