The unitary analogue of Pillai’s arithmetical functions. II

László Tóth
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 2, 1996, Number 2, Pages 40–46
Full paper (PDF, 277 Kb)

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Authors and affiliations

László Tóth
Department of Mathematics and Computer Science
“Babes-Bolyai” University
Str. M. Kogalniceanu 1
RO-3400 Cluj-Napoca, Romania

Abstract

Let k be a positive integer and let (a,b)_{*,k} denote the greatest k-th power divisor of a which is a unitary divisor of b. We introduce the function
\displaystyle P_k^*=\sum_{i=1}^{n^k}(i,n^k)_{*,k}

and obtain the arithmetical evaluation of it and an asymptotic formula for the summatory function of P_k^*, which improves for k = 1 an earlier result of the author.

References

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Cite this paper

Tóth, L. (1996). The unitary analogue of Pillai’s arithmetical functions. II. Notes on Number Theory and Discrete Mathematics, 2(2), 40-46.

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