A positive integer such that every positive integer at most is a sum of distinct divisors of . For example, is practical because its divisors represent every value from through .
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A practical number is a positive integer \( n \) that can be represented as a sum of distinct positive integers not exceeding \( n \). In other words, for a number to be practical, any integer up to \( n \) can be expressed as a sum of distinct integers chosen from the set of positive integers less than or equal to \( n \).