Abstract
Let $A$ be a subset of $\mathbb {N}$, and $W$ be a nonempty subset of $\mathbb {N}$. Denote by $\mathcal {F}^{\ast }(W)$ the set of all finite, nonempty subsets of $W$. For integer $g\geq 2$, let $A_{g}(W)$ be the set of all numbers of the form $ \sum _{f
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