Yangklan, Pussadee; Laohakosol, Vichian; Ruengsinsub, Pattira; Mavecha, Sukrawan Unitary analogues of some arithmetic functions. (English) Zbl 1484.11009 Thai J. Math., Spec. Iss.: IMT-GT International Conference on Mathematics, Statistics and Their Applications 2018, 127-134 (2020). Summary: A number of arithmetic functions, referred to as the generalized unitary-Euler’s totient, generalized unitary-Cohen’s totient, generalized unitary-divisor, generalized unitary-Liouville, odd-phi, and even-phi functions which generalize the classical totient, divisor and Liouville functions, are introduced in the setting of unitary convolution. Basic properties of these functions extending the existing ones are established. Results related to the problem of counting exponentially odd and exponentially even numbers are derived as applications. MSC: 11A25 Arithmetic functions; related numbers; inversion formulas Keywords:arithmetic function; unitary convolution; multiplicative function PDFBibTeX XMLCite \textit{P. Yangklan} et al., Thai J. Math., 127--134 (2020; Zbl 1484.11009) Full Text: Link References: [1] T. M. Apotsol, Introduction to Analytic Number Theory, New York, Springer, 1976. · Zbl 0335.10001 [2] R. Sivaramakrishnan, Classical Theory of Arithmetic Functions, New York and Basel, Marcel Dekker, 1989. · Zbl 0657.10001 [3] E. Cohen, Arithmetical functions associated with the unitary divisors of an integer, Math. Zeitschr, 74(1960), 66-80. · Zbl 0094.02601 [4] N.K. Rao, On the unitary analogues of certain totients. Monatsh. Math. 70(1965), 149-154. · Zbl 0139.27001 [5] R. Vaidyanathaswamy, The theory of multiplicative arithmetic functions, Trans. Amer. Math. Soc., 33(1931), 579-662. · Zbl 0002.12402 [6] P. Yangklan, P. Ruengsinsub and V. Laohakosol, Unitary convolution and generalized M¨obius function, KMITL Science and Technology Journal, 17(2016), 1-12. [7] P. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.