Let D(n) be the set of positive divisors of the positive integer n. For example, D(12) = {1,2,3,4,6,12}. For which n can we divide D(n) into k > 1 disjoint nonempty subsets such that the sums of the elements in each of the k sets are equal? For example, one such n is 12, and the sets are {2,12} and {1,3,4,6}.

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