{"schema":"vela.problem-packet.v0.1","problem":830,"statement":"We say that $a,b\\in \\mathbb{N}$ are an amicable pair if $\\sigma(a)=\\sigma(b)=a+b$. Are there infinitely many amicable pairs? If $A(x)$ counts the number of amicable $1\\leq a\\leq b\\leq x$ then is it true that\\[A(x)>x^{1-o(1)}?\\]","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A259180","name":"Amicable pairs.","terms":"220,284,1184,1210,2620,2924,5020,5564,6232,6368,10744,10856,12285,14595,17296,18416,63020,76084,66928,66992,67095,71145,","url":"https://oeis.org/A259180"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}