{"schema":"vela.problem-packet.v0.1","problem":322,"statement":"Let $k\\geq 3$ and $A\\subset \\mathbb{N}$ be the set of $k$th powers. What is the order of growth of $1_A^{(k)}(n)$, i.e. the number of representations of $n$ as the sum of $k$ many $k$th powers? Does there exist some $c>0$ and infinitely many $n$ such that\\[1_A^{(k)}(n) >n^c?\\]","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A025418","name":"Least sum of 3 positive cubes in exactly n ways.","terms":"3,251,5104,13896,161568,1296378,2016496,2562624,14926248,34012224,69190848,150547032,119095488,1204376256,952763904,1592","url":"https://oeis.org/A025418"},{"id":"A025456","name":"Number of partitions of n into 3 positive cubes.","terms":"0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,","url":"https://oeis.org/A025456"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}