{"schema":"vela.problem-packet.v0.1","problem":462,"statement":"Let $p(n)$ denote the least prime factor of $n$. There is a constant $c&#62;0$ such that\\[\\sum_{\\substack{n<x\\\\ n\\textrm{ not prime}}}\\frac{p(n)}{n}\\sim c\\frac{x^{1/2}}{(\\log x)^2}.\\]Is it true that there exists a constant $C>0$ such that\\[\\sum_{x\\leq n\\leq x+Cx^{1/2}(\\log x)^2}\\frac{p(n)}{n} \\gg 1\\]for all large $x$?","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A032742","name":"a(1) = 1; for n > 1, a(n) = largest proper divisor of n (that is, for n>1, maximum divisor d of n in range 1 <= d < n).","terms":"1,1,1,2,1,3,1,4,3,5,1,6,1,7,5,8,1,9,1,10,7,11,1,12,5,13,9,14,1,15,1,16,11,17,7,18,1,19,13,20,1,21,1,22,15,23,1,24,7,25,1","url":"https://oeis.org/A032742"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}