$p$-adic valuation of harmonic sums and their connections with Wolstenholme primes

Leonardo Carofiglio, Luigi De Filpo, Alessandro Gambini

We explore a conjecture posed by Eswarathasan and Levine on the distribution of $p$-adic valuations of harmonic numbers $H(n)=1+1/2+\cdots +1/n$ that states that the set $J_p$ of th…