For every k ≥ 4 the map p to the natural density of integers whose k-th smallest prime divisor is p fails to be unimodal.
Erdős,Some unconventional problems in number theory, Astérisque61(1979), 73–82
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A Complete Answer to Erd\H{o}s Problem 690
For every k ≥ 4 the map p to the natural density of integers whose k-th smallest prime divisor is p fails to be unimodal.