{"paper":{"title":"On a sum involving the Euler function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Hao Pan, Igor E. Shparlinski, Lixia Dai, Olivier Bordell\\`es, Randell Heyman","submitted_at":"2018-08-01T06:42:52Z","abstract_excerpt":"We obtain reasonably tight upper and lower bounds on the sum $\\sum_{n \\leqslant x} \\varphi \\left( \\left\\lfloor{x/n}\\right\\rfloor\\right)$, involving the Euler functions $\\varphi$ and the integer parts $\\left\\lfloor{x/n}\\right\\rfloor$ of the reciprocals of integers."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.00188","kind":"arxiv","version":3},"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"}