p23.erl

-module(p23).

-export([answer/0]).

%% A perfect number is a number for which the sum of its proper divisors is exactly equal to the number.
%% For example, the sum of the proper divisors of 28 would be 1 + 2 + 4 + 7 + 14 = 28, which means that 28 is a perfect number.
%% A number n is called deficient if the sum of its proper divisors is less than n and it is called abundant if this sum exceeds n.
%% As 12 is the smallest abundant number, 1 + 2 + 3 + 4 + 6 = 16, the smallest number that can be written as the sum of two
%% abundant numbers is 24. By mathematical analysis, it can be shown that all integers greater than 28123 can be written as the sum
%% of two abundant numbers. However, this upper limit cannot be reduced any further by analysis even though it is known that the
%% greatest number that cannot be expressed as the sum of two abundant numbers is less than this limit.
%% Find the sum of all the positive integers which cannot be written as the sum of two abundant numbers.

answer() ->
    find_answer(lists:seq(1, 28124), [], rbdict:new(), 0).

find_answer([], _As, _Sums, S) -> S;
find_answer([N | Ns], As, Sums, S) ->
    NewSums = case is_abundant(N) of
                  true -> NewAs = [N | As],
                          lists:foldl(fun(Sum, Acc) -> rbdict:store(Sum, true, Acc) end, Sums, lists:map(fun(X) -> X+N end, NewAs));
                  false -> NewAs = As,
                           Sums
              end,
    NewSum = case rbdict:is_key(N, NewSums) of
                 true -> S;
                 false -> S+N
             end,
    find_answer(Ns, NewAs, NewSums, NewSum).

is_abundant(N) ->
    my_math:d(N) > N.