On the Number of Subsets Relatively Prime to an Integer
نویسندگان
چکیده
A nonempty subset A of {1, 2, . . . , n} is said to be relatively prime if gcd(A) = 1. Nathanson [4] defined f(n) to be the number of relatively prime subsets of {1, 2, . . . , n} and, for k ≥ 1, fk(n) to be the number of relatively prime subsets of {1, 2, . . . , n} of cardinality k. Nathanson [4] defined Φ(n) to be the number of nonempty subsets A of the set {1, 2, . . . , n} such that gcd(A) is relatively prime to n and, for integer k ≥ 1, Φk(n) to be the number of subsets A of the set {1, 2, . . . , n} such that gcd(A) is relatively prime to n and card(A) = k.
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