{"schema":"vela.problem-packet.v0.1","problem":148,"statement":"Let $F(k)$ be the number of solutions to\\[ 1= \\frac{1}{n_1}+\\cdots+\\frac{1}{n_k},\\]where $1\\leq n_1&#60;\\cdots&#60;n_k$ are distinct integers. Find good estimates for $F(k)$.","status":"open","seam":"sealed","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[{"id":"att_ff09c3859e3d7ff0","kind":"transfer","claim":"Transfer from #306: exact F(k) (number of representations of 1 by k distinct unit fractions) for k<=7 = [F(1)=1,F(2)=0,F(3)=1,F(4)=6,F(5)=72,F(6)=2320,F(7)=245765]; split-tree lower-bound table.","grade":"verified_reduction","gateStatus":"needs_verification","superseded":false}],"velaLean":[],"oeis":[{"id":"A006585","name":"Egyptian fractions: number of solutions to 1 = 1/x_1 + ... + 1/x_n in positive integers x_1 < ... < x_n.","terms":"1,0,1,6,72,2320,245765,151182379","url":"https://oeis.org/A006585"},{"id":"A076393","name":"Decimal expansion of Vardi constant arising in the Sylvester sequence.","terms":"1,2,6,4,0,8,4,7,3,5,3,0,5,3,0,1,1,1,3,0,7,9,5,9,9,5,8,4,1,6,4,6,6,9,4,9,1,1,1,4,5,6,0,1,7,9,2,0,9,0,6,5,5,3,3,1,5,3,4,5,","url":"https://oeis.org/A076393"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}