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Unitary analogues of a generalized number-theoretic sum
Traiwat Intarawong,Boonrod Yuttanan 대한수학회 2023 대한수학회논문집 Vol.38 No.2
In this paper, we investigate the sums of the elements in the finite set $\{x^{k}:1\leq x\leq\frac{n}{m},\gcd_u(x,n)=1\}$, where $k$, $m$ and $n$ are positive integers and $\gcd_u(x,n)$ is the unitary greatest common divisor of $x$ and $n$. Moreover, for some cases of $k$ and $m$, we can give the explicit formulae for the sums involving some well-known arithmetic functions.