Composite numbers dividing binomial coefficients

Let kk be the number of composite integers nn that satisfy the condition that nn is a factor of (nr)\dbinom{n}{r} for all r{1,2,3,,n1}.r\in \{ 1, 2, 3, \ldots, n-1\}. Which one of the following statements is always true for kk? Prove that your answer is right.

Note: An integer number is called composite if it is greater than 1 and has at least a factor that is different from 1 and from itself.

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