For each integer m at least 2, the weighted sum of the generalized Liouville function λ_m over integers whose smallest prime factor has a given Frobenius conjugacy class equals the expected density |C|/|G|.
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An analogue of a formula for Chebotarev Densities
For each integer m at least 2, the weighted sum of the generalized Liouville function λ_m over integers whose smallest prime factor has a given Frobenius conjugacy class equals the expected density |C|/|G|.