{"schema":"vela.problem-packet.v0.1","problem":371,"statement":"Let $P(n)$ denote the largest prime factor of $n$. Show that the set of $n$ with $P(n)&#60;P(n+1)$ has density $1/2$.","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A070089","name":"P(n) < P(n+1) where P(n) (A006530) is the largest prime factor of n.","terms":"1,2,4,6,8,9,10,12,16,18,20,21,22,24,25,27,28,30,32,33,36,40,42,45,46,48,50,52,54,56,57,58,60,64,66,68,70,72,75,77,78,81,","url":"https://oeis.org/A070089"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}