{"schema":"vela.problem-packet.v0.1","problem":768,"statement":"Let $A\\subset\\mathbb{N}$ be the set of $n$ such that for every prime $p\\mid n$ there exists some $d\\mid n$ with $d>1$ such that $d\\equiv 1\\pmod{p}$. Is it true that there exists some constant $c>0$ such that for all large $N$\\[\\frac{\\lvert A\\cap [1,N]\\rvert}{N}=\\exp(-(c+o(1))\\sqrt{\\log N}\\log\\log N).\\]","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A001034","name":"Orders of noncyclic simple groups (without repetition).","terms":"60,168,360,504,660,1092,2448,2520,3420,4080,5616,6048,6072,7800,7920,9828,12180,14880,20160,25308,25920,29120,32736,3444","url":"https://oeis.org/A001034"},{"id":"A352287","name":"Numbers k such that, for every prime p dividing k, k has a nontrivial divisor which is congruent to 1 (mod p).","terms":"1,12,24,30,36,48,56,60,72,80,90,96,105,108,112,120,132,144,150,160,168,180,192,210,216,224,240,252,264,270,280,288,300,3","url":"https://oeis.org/A352287"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}