1 School of Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, P. R. China
2 School of Mathematical Sciences and Institute of Mathematics, Nanjing Normal University, Nanjing 210023, P. R. China and School of Mathematics and Statistics, Anhui Normal University, Wuhu 241003, P. R. China
Let Hn be the n-th harmonic number and let vn be its denominator. It is known that vn is even for every integer . In this paper, we study the properties of Hn and prove that for any integer n, vn = en(1+o(1)). In addition, we obtain some results of the logarithmic density of harmonic numbers.
Boyd, D. W., A p-adic study of the partial sums of the harmonic series, Exp. Math., 3(4) (1994), 287–302.