[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/CKMS.c180414

GENERALIZATIONS OF NUMBER-THEORETIC SUMS

Kanasri, Narakorn Rompurk (Department of Mathematics Khon Kaen University)
Pornsurat, Patchara (Department of Mathematics Khon Kaen University)
Tongron, Yanapat (Department of Mathematics Khon Kaen University)

Publication Information

Communications of the Korean Mathematical Society / v.34, no.4, 2019 , pp. 1105-1115 More about this Journal

Abstract

For positive integers n and k, let $S_k(n)$ and $S^{\prime}_k(n)$ be the sums of the elements in the finite sets { $x^k:1{\leq}x{\leq}n$ , (x, n) = 1} and { $x^k:1{\leq}x{\leq}n/2$ , (x, n) = 1}respectively. The formulae for both $S_k(n)$ and $S^{\prime}_k(n)$ are established. The explicit formulae when k = 1, 2, 3 are also given.

Keywords

arithmetic function; Euler's phi-function; $M{\ddot{o}}bius$ function; $M{\ddot{o}}bius$ inversion formula; sum of power of integers;

Citations & Related Records

Reference

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