{"schema":"vela.problem-packet.v0.1","problem":304,"statement":"For integers $1\\leq a&#60;b$ let $N(a,b)$ denote the minimal $k$ such that there exist integers $1&#60;n_1&#60;\\cdots&#60;n_k$ with\\[\\frac{a}{b}=\\frac{1}{n_1}+\\cdots+\\frac{1}{n_k}.\\]Estimate $N(b)=\\max_{1\\leq a&#60;b}N(a,b)$. Is it true that $N(b) \\ll \\log\\log b$?","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A097847","name":"Triangle read by rows: T(n,k) = minimal number of terms needed to write k/n (for 1 <= k <= n) as a sum of unit fractions.","terms":"1,1,1,1,2,1,1,1,2,1,1,2,2,3,1,1,1,1,2,2,1,1,2,3,2,3,3,1,1,1,2,1,2,2,3,1,1,2,1,2,2,2,3,3,1,1,1,2,2,1,2,2,3,3,1,1,2,2,2,3,","url":"https://oeis.org/A097847"},{"id":"A097849","name":"Maximal entry in row n of A097847.","terms":"1,1,2,2,3,2,3,3,3,3,4,3,4,4,3,4,5,3,4,3,4,4,5,3,4,4,4,4,5,4,5,4,4,5,4,4,5,5,5,4,5,4,5,4,4,5,5,4,5,5,5,5,5,4,5,4,5,5,5,4,","url":"https://oeis.org/A097849"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}