The number L(a, b) = a−b ln a−ln b for a 6= b and L(a, a) = a, is said to be the logarithmic mean of the positive numbers a, b. We shall say that a sequence (an) ∞ n=1 with positive terms is a… (More)

In this paper we study sequences of the form (a + b)∞n=1, where a, b ∈ N. We prove many interesting results connection with sequences with infinitely many prime divisors.