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Let $r\ge k\ge 2$ be fixed positive integers. Let $\varrho_{r,k}$ denote thecharacteristic function of the set of $r$-tuples of positive integers with$k$-wise relatively prime components, that is any $k$ of them are relativelyprime. We use the convolution method to establish an asymptotic formula for thesum $\sum_{n_1,\ldots,n_r\le x} \varrho_{r,k}(n_1,\ldots,n_r)$ by elementaryarguments. Our result improves the error term obtained by J. Hu (2013).

Counting $r$-tuples of positive integers with $k$-wise relatively prime components