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Unitary analogues of some arithmetic functions. (English) Zbl 1484.11009

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
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References:

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