{"schema":"vela.problem-packet.v0.1","problem":1060,"statement":"Let $f(n)$ count the number of solutions to $k\\sigma(k)=n$, where $\\sigma(k)$ is the sum of divisors of $k$. Is it true that $f(n)\\leq n^{o(\\frac{1}{\\log\\log n})}$? Perhaps even $\\leq (\\log n)^{O(1)}$?","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A327153","name":"Number of divisors d of n such that sigma(d)*d is equal to n.","terms":"1,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,","url":"https://oeis.org/A327153"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}