An Arithmetic Function and the k-th Power Part of a Positive Integer

Ming Jun Wang

doi:10.4028/www.scientific.net/AMR.490-495.1941

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HomeAdvanced Materials ResearchAdvanced Materials Research Vols. 490-495An Arithmetic Function and the k-th Power Part of...

An Arithmetic Function and the k-th Power Part of a Positive Integer

Abstract:

For any positive integer denotes the largest - power less than or equal to ,and denotes the smallest - power greater than or equal to . Let be a prime, denotes the large exponent of power which divides .In this paper we use elementary method to study the mean value properties of and ,and give two interesting asymptotic formulas.

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Periodical:

Advanced Materials Research (Volumes 490-495)

Pages:

1941-1944

DOI:

https://doi.org/10.4028/www.scientific.net/AMR.490-495.1941

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Online since:

March 2012

Authors:

Ming Jun Wang

Keywords:

Arithmetic Function, Asymptotic Formula, k-th Power, Mean Value

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References

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