primeFactorisation.scala

def factorise(l: Long): Map[Long, Int] = {
  def innerFactorise(l: Long, primes: List[Long], factors: List[Long]): List[Long] = {
    def expandPrimes: List[Long] = {
      def innerExpand(candidate: Long): List[Long] = {
        val maxFactor = Math.sqrt(candidate).toLong + 1l
        val factors = primes.takeWhile(_ < maxFactor).dropWhile(candidate % _ != 0)
        if (factors.isEmpty) primes ::: candidate :: Nil else innerExpand(candidate + 1)
      }
      innerExpand(primes.last + 1)
    }
    primes.last match {
      case x if (x == l) => (x :: factors).reverse
      case x if (l % x == 0) => innerFactorise(l / x, primes, x :: factors)
      case _ => innerFactorise(l, expandPrimes, factors)
    }
  }
  innerFactorise(l, List(2), Nil).foldLeft(Map.empty[Long, Int]) {(acc, next) =>
    acc(next) = acc.getOrElse(next, 0) + 1
  }
}