Asymptotic estimates for phi functions for subsets of {m+1, m+2,...,n}

Details Asymptotic estimates for phi functions for subsets of {m+1, m+2,...,n} Asymptotic estimates for phi functions for subsets of {m+1, m+2,...,n}

2007-09-18

arxiv.org/abs/0709.2930v1

Mathematics

Number Theory

5 pages

Scientific paper

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 f_k(m,n) and Phi_k(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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