51 lines
1.6 KiB
Plaintext
51 lines
1.6 KiB
Plaintext
defmodule Proper do
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def divisors(1), do: []
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def divisors(n), do: [1 | divisors(2,n,:math.sqrt(n))] |> Enum.sort
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defp divisors(k,_n,q) when k>q, do: []
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defp divisors(k,n,q) when rem(n,k)>0, do: divisors(k+1,n,q)
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defp divisors(k,n,q) when k * k == n, do: [k | divisors(k+1,n,q)]
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defp divisors(k,n,q) , do: [k,div(n,k) | divisors(k+1,n,q)]
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end
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defmodule Aliquot do
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def sequence(n, maxlen\\16, maxterm\\140737488355328)
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def sequence(0, _maxlen, _maxterm), do: "terminating"
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def sequence(n, maxlen, maxterm) do
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{msg, s} = sequence(n, maxlen, maxterm, [n])
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{msg, Enum.reverse(s)}
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end
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defp sequence(n, maxlen, maxterm, s) when length(s) < maxlen and n < maxterm do
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m = Proper.divisors(n) |> Enum.sum
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cond do
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m in s ->
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case {m, List.last(s), hd(s)} do
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{x,x,_} ->
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case length(s) do
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1 -> {"perfect", s}
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2 -> {"amicable", s}
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_ -> {"sociable of length #{length(s)}", s}
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end
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{x,_,x} -> {"aspiring", [m | s]}
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_ -> {"cyclic back to #{m}", [m | s]}
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end
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m == 0 -> {"terminating", [0 | s]}
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true -> sequence(m, maxlen, maxterm, [m | s])
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end
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end
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defp sequence(_, _, _, s), do: {"non-terminating", s}
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end
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Enum.each(1..10, fn n ->
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{msg, s} = Aliquot.sequence(n)
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:io.fwrite("~7w:~21s: ~p~n", [n, msg, s])
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end)
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IO.puts ""
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[11, 12, 28, 496, 220, 1184, 12496, 1264460, 790, 909, 562, 1064, 1488, 15355717786080]
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|> Enum.each(fn n ->
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{msg, s} = Aliquot.sequence(n)
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if n<10000000, do: :io.fwrite("~7w:~21s: ~p~n", [n, msg, s]),
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else: :io.fwrite("~w: ~s: ~p~n", [n, msg, s])
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end)
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