Order the Integers

Let \(f(n)\) be the number of ways the first \(n\) natural numbers, from \(1\) to \(n\), can be ordered such that every number in the permutation divides the sum of the previous numbers.

Find \(f(19)\)

  • Example: One way to arrange the first 6 natural numbers in this way is [4, 1, 5, 2, 6, 3]
  • Clarification: Calculating \(f(19)\) takes about \(16\) seconds in a Haskell program. For a bonus challenge, try devising a method that calculates \(f(n)\) for values higher than 30
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