# 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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