{"schema":"vela.problem-packet.v0.1","problem":69,"statement":"Is\\[\\sum_{n\\geq 2}\\frac{\\omega(n)}{2^n}\\]irrational? (Here $\\omega(n)$ counts the number of distinct prime divisors of $n$.)","status":"solved","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A262153","name":"Decimal expansion of Sum_{p prime} 1/(2^p-1), a prime equivalent of the Erdős-Borwein constant.","terms":"5,1,6,9,4,2,8,1,9,8,0,5,6,4,0,3,8,4,2,4,0,5,1,6,6,0,8,4,7,9,8,5,6,2,7,7,9,7,8,5,4,6,9,4,7,9,1,3,0,9,1,2,4,1,6,5,0,2,8,0,","url":"https://oeis.org/A262153"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}