{"paper":{"title":"Multiple harmonic sums and multiple harmonic star sums are (nearly) never integers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Khodabakhsh Hessami Pilehrood, Roberto Tauraso, Tatiana Hessami Pilehrood","submitted_at":"2016-06-18T06:21:03Z","abstract_excerpt":"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, Erd\\H{o}s and Niven proved that the nested multiple harmonic sum $H_n(\\{1\\}^r)=\\sum_{1\\le k_1<\\dots<k_r\\le n}\\frac{1}{k_1\\cdots k_r}$ can take integer values only for a finite number of positive integers $n$. In 2012, Chen and Tang refined this result by showing that $H_n(\\{1\\}^r)$ is an integer only for $(n,r)=(1,1)$ and $(n,r)=(3,2)$. In this paper, we consider the integrality problem for arbitrary multiple harmonic and multiple harmonic star sums and show that none of these sums i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.05722","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}