If a set S of prime ideals has natural density δ(S), then δ(S) equals the negative limit as X goes to infinity of the sum of μ(a)/N(a) over ideals a in D(K,S) with norm at most X.
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M\"obius formulas for densities of sets of prime ideals
If a set S of prime ideals has natural density δ(S), then δ(S) equals the negative limit as X goes to infinity of the sum of μ(a)/N(a) over ideals a in D(K,S) with norm at most X.