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Iterate each possible subset

Given a set of integers $S=\{2,5,8,14,18, \dots \}$, does Mathematica have a way to iterate each subset (i.e. all subsets in the power set of $S$) with a loop construct? The purpose is to sum all ...
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Nested For Loops that result in no output [duplicate]

I am sure that this is not the most elegant code you will have seen, but I am trying to loop through an expression to see if FultonHarrisn] produces any outputs ...