The Number of Relatively Prime Subsets Of
نویسندگان
چکیده
A nonempty subset A ⊆ {1, 2 . . . , n} is relatively prime if gcd(A) = 1. Let f(n) denote the number of relatively prime subsets of {1, 2 . . . , n}. The sequence given by the values of f(n) is sequence A085945 in Sloane’s On-Line Encyclopedia of Integer Sequences. In this article we show that f(n) is never a square if n ≥ 2. Moreover, we show that reducing the terms of this sequence modulo any prime l #= 3 leads to a sequence which is not periodic modulo l.
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