We consider two problems regarding some divisibility properties of the subset sums of a set A ⊆ {1, 2, . . . , n}. At the beginning, we study the cardinality of A which has the following property: For every d ≤ n there is a non empty set A d ⊆ A such that the sum of the elements of A d is a multiple of d. Next, we turn our attention to another problem: If all subset sums of A form a multiple free-sequence, what can we say about the structure of A? We give some asymptotics for the first problem and improve some already existing results for the second one.
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