Abstract
Two classes of finite linear sums concerning the floor function and three arithmetic functions are evaluated in closed forms.
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References
M. Bai, W. Chu, and N. N. Li, “Generalization of an identity about Euler’s totient function,” Bull. Irish Math. Soc. 83, 5–7 (2019).
M. A. Alekseyev, “Problems and Solutions,” Amer. Math. Monthly 118 (1), 84–91 (2011); “Problems and Solutions,” Amer. Math. Monthly 119 (9), 800–807 (2012).
L. Comtet, Advanced Combinatorics (D. Reidel Publ., Dordrecht, 1974).
W. Chu, “Jordan’s totient function and trigonometric sums,” Studia Sci. Math. Hungar. 57 (1), 40–53 (2020).
R. Dineva, The Euler Totient, the Möbius and the Divisor Functions, arXiv: http://www. mtholyoke. edu/~robinson/reu/reu05/rdineva1.pdf.
N. Pabhapote and V. Laohakoso, “Combinatorial aspects of the generalized EulerTs totient,” Int. J. Math. Math. Sci. 2010, Article ID 648165 (2010).
R. S. Lehman, “On Liouville’s Function,” Math. Comput. 14, 311–320 (1960).
R. L. Graham, D. E. Knuth, and O. Patashnik, Concrete Mathematics (Addison-Wesley Publ., Reading, MA, 1989).
D. M. Burton, Elementary Number Theory (McGraw-Hill, Boston, MA, 2007).
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The author is sincerely grateful to the referee for the careful reading, critical comments and helpful suggestions that contribute significantly to improve the manuscript during the revision.
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Translated from Matematicheskie Zametki, 2022, Vol. 112, pp. 371–375 https://doi.org/10.4213/mzm13659.
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Chu, W. Linear Sums on the Floor Function and Three Arithmetic Functions. Math Notes 112, 378–381 (2022). https://doi.org/10.1134/S000143462209005X
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DOI: https://doi.org/10.1134/S000143462209005X