{"schema":"vela.problem-packet.v0.1","problem":468,"statement":"For any $n$ let $D_n$ be the set of sums of the shape $d_1,d_1+d_2,d_1+d_2+d_3,\\ldots$ where $1<d_1<d_2<\\cdots$ are the divisors of $n$. What is the size of $D_n\\backslash \\cup_{m<n}D_m$?If $f(N)$ is the minimal $n$ such that $N\\in D_n$ then is it true that $f(N)=o(N)$? Perhaps just for almost all $N$?","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A167485","name":"Smallest positive integer m such that n can be expressed as the sum of an initial subsequence of the divisors of m, or 0 if no such m exists.","terms":"1,1,0,2,3,0,5,4,7,15,12,21,6,9,13,8,12,30,10,42,19,18,20,57,14,36,46,30,12,102,29,16,21,42,62,84,22,36,37,18,27,63,20,50","url":"https://oeis.org/A167485"},{"id":"A387502","name":"Number of debut sums of initial subsequences of the divisors > 1 of n.","terms":"0,1,1,1,1,1,1,1,1,1,0,3,1,1,1,1,0,2,1,2,2,1,0,1,0,0,1,1,1,3,0,1,1,1,0,4,1,0,0,2,0,3,1,1,1,1,0,3,1,2,0,2,0,2,0,1,2,0,0,3,","url":"https://oeis.org/A387502"},{"id":"A387503","name":"Total number of distinct sums of initial subsequences of the divisors > 1 of positive integers up to n.","terms":"0,1,2,3,4,5,6,7,8,9,9,12,13,14,15,16,16,18,19,21,23,24,24,25,25,25,26,27,28,31,31,32,33,34,34,38,39,39,39,41,41,44,45,46","url":"https://oeis.org/A387503"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}