Among all nonempty subsets of {0,...,k}, the interval {1,...,k} maximizes the number of additive divisors, and the all-ones number maximizes lunar divisors in every base.
Additive decomposability of multiplicatively defin ed sets
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Maximally additively reducible subsets of the integers
Among all nonempty subsets of {0,...,k}, the interval {1,...,k} maximizes the number of additive divisors, and the all-ones number maximizes lunar divisors in every base.