Keywords: Euler totient function; generalized gcd; Jordan totient function; Klee's function
@article{10_21136_CMJ_2021_0370_20,
author = {Chandran, Arya and Thomas, Neha Elizabeth and Namboothiri, K. Vishnu},
title = {A {Menon-type} identity using {Klee's} function},
journal = {Czechoslovak Mathematical Journal},
pages = {165--176},
year = {2022},
volume = {72},
number = {1},
doi = {10.21136/CMJ.2021.0370-20},
mrnumber = {4389112},
zbl = {07511559},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2021.0370-20/}
}
TY - JOUR AU - Chandran, Arya AU - Thomas, Neha Elizabeth AU - Namboothiri, K. Vishnu TI - A Menon-type identity using Klee's function JO - Czechoslovak Mathematical Journal PY - 2022 SP - 165 EP - 176 VL - 72 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2021.0370-20/ DO - 10.21136/CMJ.2021.0370-20 LA - en ID - 10_21136_CMJ_2021_0370_20 ER -
%0 Journal Article %A Chandran, Arya %A Thomas, Neha Elizabeth %A Namboothiri, K. Vishnu %T A Menon-type identity using Klee's function %J Czechoslovak Mathematical Journal %D 2022 %P 165-176 %V 72 %N 1 %U http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2021.0370-20/ %R 10.21136/CMJ.2021.0370-20 %G en %F 10_21136_CMJ_2021_0370_20
Chandran, Arya; Thomas, Neha Elizabeth; Namboothiri, K. Vishnu. A Menon-type identity using Klee's function. Czechoslovak Mathematical Journal, Tome 72 (2022) no. 1, pp. 165-176. doi: 10.21136/CMJ.2021.0370-20
[1] Apostol, T. M.: Introduction to Analytic Number Theory. Undergraduate Texts in Mathematics. Springer, New York (1976). | DOI | MR | JFM
[2] Cohen, E.: Some totient functions. Duke Math. J. 23 (1956), 515-522. | DOI | MR | JFM
[3] Haukkanen, P.: Menon's identity with respect to a generalized divisibility relation. Aequationes Math. 70 (2005), 240-246. | DOI | MR | JFM
[4] Haukkanen, P., Tóth, L.: Menon-type identities again: A note on a paper by Li, Kim and Qiao. Publ. Math. 96 (2020), 487-502. | DOI | MR | JFM
[5] Haukkanen, P., Wang, J.: A generalization of Menon's identity with respect to a set of polynomials. Port. Math. 53 (1996), 331-337. | MR | JFM
[6] Jordan, C.: Traité des substitutions et des équations algébriques. Gauthier-Villars, Paris (1870), French \99999JFM99999 03.0042.02. | MR
[7] Menon, P. Kesava: On the sum $\sum (a-1,n),[(a,n)=1]$. J. Indian Math. Soc., New Ser. 29 (1965), 155-163. | MR | JFM
[8] Klee, V. L.: A generalization of Euler's $\varphi$-function. Am. Math. Mon. 55 (1948), 358-359. | DOI | MR | JFM
[9] Li, Y., Kim, D.: A Menon-type identity with many tuples of group of units in residually finite Dedekind domains. J. Number Theory 175 (2017), 42-50. | DOI | MR | JFM
[10] Miguel, C.: A Menon-type identity in residually finite Dedekind domains. J. Number Theory 164 (2016), 43-51. | DOI | MR | JFM
[11] Rao, K. Nageswara: On certain arithmetical sums. Theory of Arithmetic Functions Lecture Notes in Mathematics 251. Springer, Berlin (1972), 181-192. | DOI | MR | JFM
[12] Ramaiah, V. Sita: Arithmetical sums in regular convolutions. J. Reine Angew. Math. 303/304 (1978), 265-283. | DOI | MR | JFM
[13] Sivaramakrishnan, R.: Classical Theory of Arithmetic Functions. Pure and Applied Mathematics 126. Marcel Dekker, New York (1989). | MR | JFM
[14] Sury, B.: Some number-theoretic identities from group actions. Rend. Circ. Mat. Palermo (2) 58 (2009), 99-108. | DOI | MR | JFM
[15] Tărnăuceanu, M.: A generalization of the Euler's totient function. Asian-Eur. J. Math. 8 (2015), Artile ID 1550087, 13 pages. | DOI | MR | JFM
[16] Tóth, L.: Menon's identity and arithmetical sums representing functions of several variables. Rend. Semin. Mat., Univ. Politec. Torino 69 (2011), 97-110. | MR | JFM
[17] Tóth, L.: Menon-type identities concerning Dirichlet characters. Int. J. Number Theory 14 (2018), 1047-1054. | DOI | MR | JFM
[18] Tóth, L.: Short proof and generalization of a Menon-type identity by Li, Hu and Kim. Taiwanese J. Math. 23 (2019), 557-561. | DOI | MR | JFM
[19] Zhao, X.-P., Cao, Z.-F.: Another generalization of Menon's identity. Int. J. Number Theory 13 (2017), 2373-2379. | DOI | MR | JFM
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