Multiple harmonic sums and multiple harmonic star sums are (nearly) never integers

Khodabakhsh Hessami Pilehrood, Tatiana Hessami Pilehrood, Roberto Tauraso

It is well known that the harmonic sum $H_n(1)={\sum }_{k=1}^n\frac{1}{k}$ is never an integer for $n>1$. In 1946, Erdős and Niven proved that the nested multiple harmonic sum $H_n(\{…