Affine Invariants , Relatively Prime Sets , and a Phi Function for Subsets of { 1 , 2 , . . . , N }
نویسنده
چکیده
A nonempty subset A of {1, 2, . . . , n} is relatively prime if gcd(A) = 1. Let f(n) and fk(n) denote, respectively, the number of relatively prime subsets and the number of relatively prime subsets of cardinality k of {1, 2, . . . , n}. Let Φ(n) and Φk(n) denote, respectively, the number of nonempty subsets and the number of subsets of cardinality k of {1, 2, . . . , n} such that gcd(A) is relatively prime to n. Exact formulas and asymptotic estimates are obtained for these functions.
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