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For an integer n≯1 letP(n) be the largest prime factor of n. We prove that there are infinitely many triplets of consecutive integers with descending largest prime factors, that is P(n - 1) ≯P(n)≯P(n+1) occurs for infinitely many integers n.
Community structure (species richness, dominance, similarity, diversity and seasonal dynamics) of the rove beetles (Staphylinidae) was examined in an abandoned, a conventional and an organic vineyard management plot of an experimental vineyard in Hungary.During the survey, a total number of 493 specimens belonging to 33 species were collected by pitfall traps. The dominant species were Sphenoma togata, Xantholinus linearis and Pseudocypus penetrans that presented 76.66% of all staphylinids collected in the vineyard. All of the most common staphylinid species had only one generation per year and overwintered as adults.There were significant differences in species richness and abundance; both were the highest in the abandoned plot. The dissimilarity in species composition between the differently treated plots was also high. The diversity was the highest in organic, and the lowest in conventionally treated plot, while the abandoned one showed an intermediate value.
