{"schema":"vela.problem-packet.v0.1","problem":252,"statement":"Let $k\\geq 1$ and $\\sigma_k(n)=\\sum_{d\\mid n}d^k$. Is\\[\\sum \\frac{\\sigma_k(n)}{n!}\\]irrational?","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A227988","name":"Decimal expansion of Sum_{n >= 1} sigma_1(n)/n!.","terms":"3,5,2,7,0,0,0,4,7,1,8,5,2,9,5,2,8,2,9,7,6,1,5,3,6,7,9,1,7,6,9,3,2,6,2,0,3,7,6,3,5,6,4,3,4,4,9,5,2,4,0,8,2,7,7,6,0,5,7,1,","url":"https://oeis.org/A227988"},{"id":"A227989","name":"Decimal expansion of Sum_{n >= 1} sigma_2(n)/n!.","terms":"6,3,4,0,0,9,6,6,6,8,8,9,2,1,7,1,6,3,8,8,2,9,9,6,5,9,9,4,0,0,7,5,0,4,6,0,7,8,6,3,6,4,4,3,3,5,5,9,8,9,0,1,7,8,5,4,3,9,9,6,","url":"https://oeis.org/A227989"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}