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
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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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