object Bud {
def buddy(start: Long, limit: Long): String = {
    case class Memo[A,B](f: A => B) extends (A => B) {
      import scala.collection.mutable
      private val cache = mutable.Map.empty[A, B]
      def apply(x: A):B = cache.getOrElseUpdate(x, f(x))
    }

    def s(n: Long): Long = {
      (1L to (math.sqrt(n)+0.5).toLong).view.filter(n % _ == 0).flatMap(x => Seq(x, n/x)).distinct.sum - n
    }

    lazy val f = Memo[Long, Long](s)

    (start to limit).find(n => f(n)>n+1 && n== f(f(n)-1) - 1) match {
      case Some(x) =>
        s"($x ${f(x)-1})"
      case None => "Nothing"
    }
  }
}