Average of certain multiplicative functions over integers without small and large prime factors

Abstract. Song (2001) described the asymptotic behaviour of sums including certain nonnegative multiplicative functions, where the summation runs over the integers without large prime factors. We generalise the method to restrict the summation to integers without small and large prime factors.

Key words and phrases. Integers free of small prime factors, integers free of large prime factors, nonnegative multiplicative function, summation.