{"schema":"vela.problem-packet.v0.1","problem":1054,"statement":"Let $f(n)$ be the minimal integer $m$ such that $n$ is the sum of the $k$ smallest divisors of $m$ for some $k\\geq 1$.Is it true that $f(n)=o(n)$? Or is this true only for almost all $n$, and $\\limsup f(n)/n=\\infty$?","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"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}