{"paper":{"title":"Piatetski-Shapiro sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Andreas J. Weingartner, Igor E. Shparlinski, J\\\"org Br\\\"udern, Roger C. Baker, William D. Banks","submitted_at":"2012-03-27T07:31:35Z","abstract_excerpt":"We consider various arithmetic questions for the Piatetski-Shapiro sequences $\\fl{n^c}$ ($n=1,2,3,...$) with $c>1$, $c\\not\\in\\N$. We exhibit a positive function $\\theta(c)$ with the property that the largest prime factor of $\\fl{n^c}$ exceeds $n^{\\theta(c)-\\eps}$ infinitely often. For $c\\in(1,\\tfrac{149}{87})$ we show that the counting function of natural numbers $n\\le x$ for which $\\fl{n^c}$ is squarefree satisfies the expected asymptotic formula. For $c\\in(1,\\tfrac{147}{145})$ we show that there are infinitely many Carmichael numbers composed entirely of primes of the form $p=\\fl{n^c}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.5884","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"}