{"paper":{"title":"Propri\\'et\\'es multiplicatives des entiers friables translat\\'es","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Sary Drappeau","submitted_at":"2013-07-16T11:50:51Z","abstract_excerpt":"An integer is said to be $y$-friable if its greatest prime factor P(n) is less than $y$. In this paper, we study numbers of the shape $n-1$ when $P(n)\\leq y$ and $n\\leq x$. One expects that, statistically, their multiplicative behaviour resembles that of all integers less than $x$. Extending a result of Basquin, we estimate the mean value over shifted friable numbers of certain arithmetic functions when $(\\log x)^c \\leq y$ for some positive $c$, showing a change in behaviour according to whether $\\log y / \\log\\log x$ tends to infinity or not. In the same range in $(x, y)$, we prove an Erd\\\"os-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.4250","kind":"arxiv","version":2},"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"}