On certain properties of harmonic numbers On certain properties of harmonic numbers. Let Hn be the n th harmonic number and let un be its numerator. For any prime p , let Jp be the set of positive integers n with pun. In 1991, Eswarathasan and Levine conjectured that Jp is finite for any prime p. It is clear that the p adic valuation of Hn is not less than −⌊logpn⌋. Let Tp be the set of positive integers n such that the p adic valuation of Hn is equal to −⌊logpn⌋. Article DOI: 10.1016/j.jnt.2016.11.027 Contributed by: Charles Johnson

