p12.erl

-module(p12).

-export([answer/0, triangle_iterator/0]).

%% The sequence of triangle numbers is generated by adding the natural numbers.
%% So the 7^(th) triangle number would be 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28. The first ten terms would be:
%% 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...
%% Let us list the factors of the first seven triangle numbers:
%%   1: 1
%%   3: 1, 3
%%   6: 1, 2, 3, 6
%%  10: 1, 2, 5, 10
%%  15: 1, 3, 5, 15
%%  21: 1, 3, 7, 21
%%  28: 1, 2, 4, 7, 14, 28
%% We can see that 28 is the first triangle number to have over five divisors.
%% What is the value of the first triangle number to have over five hundred divisors?

answer() ->
    TriNums = triangle_iterator(),
    find_factors(TriNums(), 501).

find_factors([Tri | Next], NumFactors) ->
    FoundFactors = count_factors(Tri),
    case FoundFactors < NumFactors of
        true ->  find_factors(Next(), NumFactors);
        _Else -> Tri
    end.

count_factors(N) ->
    lists:foldl(fun({_Prime, C}, Acc) -> Acc*(C+1) end, 1, primes:prime_factors(N)).

triangle_iterator() ->
    fun() -> tri_iter(2, 1) end.
% N is the next Tri#< whereas Tri is the current Tri#
tri_iter(N, Tri) ->
    [ Tri | fun() -> tri_iter(N+1, N+Tri) end ].