Irrationality measures for continued fractions with arithmetic functions

Abstract

Let f(n) or the base-2 logarithm of f(n) be either d(n) (the divisor function), ?(n) (the divisor-sum function), ?(n) (the Euler totient function), ?(n) (the number of distinct prime factors of n) or ?(n) (the total number of prime factors of n). We present good lower bounds for |M/N ? ?| in terms of N, where ? = [0; f(1), f(2),...].