Abstract
We prove that the number of positive integers \(n\le x\), such that \(\phi (1)+\phi (2)+\cdots +\phi (n)\) is a multiple of n, is less than \(x/(\log x)^{0.15742}\) for all sufficiently large x, where \(\phi \) stands for the Euler totient function.
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This work was supported by the National Natural Science Foundation of China (Nos. 11371195 and 11571174) and PAPD.
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Gong, ML., Chen, YG. On the average value of the first n values of the Euler function. Bol. Soc. Mat. Mex. 24, 301–306 (2018). https://doi.org/10.1007/s40590-017-0164-8
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DOI: https://doi.org/10.1007/s40590-017-0164-8