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On the Mean Value of an Arithmetical Function

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Book cover Advances in Computer Science and Information Engineering

Part of the book series: Advances in Intelligent and Soft Computing ((AINSC,volume 168))

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Abstract

Let p be a prime , e p (n) denote the largest exponent of power p which divides n . In this paper, we use elementary and analytic methods to study the asymptotic properties of ∑  n ≤ x e p (n) ϕ (n), and give an interesting asymptotic formula for it.

Foundation project: Scientific Research Program Funded by Shaanxi Provincial Education Department (11JK0485) and he students of innovation projects of Weinan Teachers University (11XK052) Education Reform Project of Weinan Teachers University (JG201132).

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Author information

Authors and Affiliations

  1. College of Mathematics and Information Science, Weinan Teachers University, Weinan, Shaanxi, 714000, China

    MingShun Yang & YaJuan Tu

Authors
  1. MingShun Yang
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  2. YaJuan Tu
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Corresponding author

Correspondence to MingShun Yang .

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Editors and Affiliations

  1. Wuhan Section of ISER Association, Guangshan Road 76, Wuhan, 430072, China, People's Republic

    David Jin

  2. Researcher Association, Guangzhou Section, International Science & Education, Jinheng Road, Jinbi Garden 85-1102 144, Guang Zhou, China, People's Republic

    Sally Lin

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© 2012 Springer-Verlag GmbH Berlin Heidelberg

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Yang, M., Tu, Y. (2012). On the Mean Value of an Arithmetical Function. In: Jin, D., Lin, S. (eds) Advances in Computer Science and Information Engineering. Advances in Intelligent and Soft Computing, vol 168. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30126-1_23

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  • DOI: https://doi.org/10.1007/978-3-642-30126-1_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-30125-4

  • Online ISBN: 978-3-642-30126-1

  • eBook Packages: EngineeringEngineering (R0)

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