On divisibility of the numbers H_n(1), H_n(2) and H_n(3) - Seibert, Jaroslav; Trojovský, Pavel (Annales Mathematicae Silesianae, 2003)
We will deal with numbers given by the relation Hn(k) = [(k+1)n-\binom{n}{2}k2-nk-1]/k3, where k is equal to 1, 2 or 3. These numbers arise from a generalization Bernoulli's inequality. In this paper some results about divisibility and primality of the numbers Hn(l), Hn(2) and Hn(3) are found. For example any positive integer n>1 does not divide Hn(2) and n ≡ 2mod4 is the necessary condition for divisibility Hn(l) and Hn(3) by n>2. In addition certain properties of their divisibility are used for finding primes among these numbers.