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sets T p ( k ) do not admit asymptotic densities. For any set S of positive integers, let the logarithmic density of S be defined by δ ( S ) = lim x → + ∞ 1 log ⁡ x ∑ n ∈ S ∩ [ 1 , x ] 1 n if the limit exists. In 2016, Sanna [ 5 ] proved that there

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