Arithmetic properties of the sum of the first \(n\) values of the Euler function

Abstract

We give an upper bound on the counting function of the set of \(n\) such that the summatory function of the Euler function up to \(n\) is a square. Our estimate improves upon a previous estimate provided by Florian Luca and A. Sankaranarayanan.

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Acknowledgments

We thank the referees for comments which improved the quality of our paper. The second author worked on this paper during Summer of 2007 when he visited the Institute for Mathematical Sciences in Chennai, India. He thanks the people of that institute for their hospitality and the TWAS for support.

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Correspondence to Florian Luca.

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Balasubramanian, R., Luca, F. & Ralaivaosaona, D. Arithmetic properties of the sum of the first \(n\) values of the Euler function. Bol. Soc. Mat. Mex. 21, 9–17 (2015). https://doi.org/10.1007/s40590-014-0045-3

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Mathematics Subject Classification

  • Primary 11N37
  • Secondary 11N36