{"schema":"vela.problem-packet.v0.1","problem":380,"statement":"We call an interval $[u,v]$ 'bad' if the greatest prime factor of $\\prod_{u\\leq m\\leq v}m$ occurs with an exponent greater than $1$. Let $B(x)$ count the number of $n\\leq x$ which are contained in at least one bad interval. Is it true that\\[B(x)\\sim \\#\\{ n\\leq x: P(n)^2\\mid n\\},\\]where $P(n)$ is the largest prime factor of $n$?","status":"solved","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A070003","name":"Numbers divisible by the square of their largest prime factor.","terms":"4,8,9,16,18,25,27,32,36,49,50,54,64,72,75,81,98,100,108,121,125,128,144,147,150,162,169,196,200,216,225,242,243,245,250,","url":"https://oeis.org/A070003"},{"id":"A387054","name":"Elements of A388654 that do not lie in A070003.","terms":"24,48,120,168,360,528,840,960,1155,1368,1680,1683,1848,1850,2208,2210,2600,2736,2737,2808,3024,3250,3480,3720,4224,4488,","url":"https://oeis.org/A387054"},{"id":"A388654","name":"Elements of an interval of natural numbers whose product is divisible by the square of the largest prime factor.","terms":"4,8,9,16,18,24,25,27,32,36,48,49,50,54,64,72,75,81,98,100,108,120,121,125,128,144,147,150,162,168,169,196,200,216,225,24","url":"https://oeis.org/A388654"},{"id":"A389100","name":"Elements of a non-singleton interval of natural numbers whose product is divisible by the square of the largest prime factor of the product.","terms":"8,9,24,25,48,49,50,120,121,168,169,242,243,288,289,360,361,528,529,675,676,840,841,960,961,1155,1156,1368,1369,1444,1445","url":"https://oeis.org/A389100"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}