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A Probabilistic Look at Series Involving Euler's Totient Function

Yung-Pin Chen
Published Online: 2012-08-01 | DOI: https://doi.org/10.1515/integers-2011-0125


We use a probabilistic method to evaluate the limit of , where is the Euler totient function and r is a nonnegative integer. We extend the probabilistic method to evaluate two other generalized types of series that involve Euler's totient function. In addition to the probabilistic method, an analytic approach is presented to evaluate the series when the exponent parameter r is a positive real number.

Keywords: Euler Totient Function; Series; Probability of Coprimality

About the article

Received: 2010-02-08

Revised: 2011-10-18

Accepted: 2012-01-12

Published Online: 2012-08-01

Published in Print: 2012-08-01

Citation Information: Integers, Volume 12, Issue 4, Pages 649–657, ISSN (Online) 1867-0652, ISSN (Print) 1867-0652, DOI: https://doi.org/10.1515/integers-2011-0125.

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© 2012 by Walter de Gruyter Berlin Boston.Get Permission

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