Asymptotic estimates for phi functions for subsets of m+1, m+2,...,n
Abstract
Let f(m,n) denote the number of relatively prime subsets of m+1,m+2,...,n, and let Phi(m,n) denote the number of subsets A of m+1,m+2,...,n such that gcd(A) is relatively prime to n. Let fk(m,n) and Phik(m,n) be the analogous counting functions restricted to sets of cardinality k. Simple explicit formulas and asymptotic estimates are obtained for these four functions.
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