{"schema":"vela.problem-packet.v0.1","problem":928,"statement":"Let $\\alpha,\\beta\\in (0,1)$ and let $P(n)$ denote the largest prime divisor of $n$. Does the density of integers $n$ such that $P(n)<n^{\\alpha}$ and $P(n+1)<(n+1)^\\beta$ exist?","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A006530","name":"Gpf(n): greatest prime dividing n, for n >= 2; a(1)=1.","terms":"1,2,3,2,5,3,7,2,3,5,11,3,13,7,5,2,17,3,19,5,7,11,23,3,5,13,3,7,29,5,31,2,11,17,7,3,37,19,13,5,41,7,43,11,5,23,47,3,7,5,1","url":"https://oeis.org/A006530"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}