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In this paper, we study the following question: what is the maximum of $|\\mathcal D(\\mathcal F)|$ for an intersecting family of $k$-element sets? Frankl conjectured that the maximum is attained when $\\mathcal F$ is the family of all sets containing a fixed element. We show that this holds if $n \\ge 50k\\ln k$ and $k \\ge 50$. 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A family $\\mathcal F$ is intersecting if any two sets from the family have non-empty intersection. In this paper, we study the following question: what is the maximum of $|\\mathcal D(\\mathcal F)|$ for an intersecting family of $k$-element sets? Frankl conjectured that the maximum is attained when $\\mathcal F$ is the family of all sets containing a fixed element. We show that this holds if $n \\ge 50k\\ln k$ and $k \\ge 50$. 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