Project Euler 12: Highly divisible triangular number

Jag löste detta problem för ett bra tag sedan men har inte skrivit något om det fram tills nu.

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?

Den naiva lösningen till detta problem är att helt enkelt generera triangeltal och dela talet med alla heltal N där 1 <= N <= talet. I praktiken behöver vi bara kolla alla faktorer mellan 1 och roten ur talet.

facs(_, Fac, NumFacs, Root) when Root  NumFacs;
facs(_, Fac, NumFacs, Root) when Root == Fac -> NumFacs + 1;
facs(Num, Fac, NumFacs, Root) when Num rem Fac == 0 ->
    facs(Num, Fac + 1, NumFacs + 2, Root);
facs(Num, Fac, NumFacs, Root) -> facs(Num, Fac + 1, NumFacs, Root).

problem_12() ->
    Start = os:timestamp(),
    Res = triangles(1, 2),
    io:format("Resultatetr ~p och det tog ~p sekunder att beräkna~n", [Res, timer:now_diff(os:timestamp(), Start)/1000000]).

triangles(Num, NewSide) ->
     case facs(Num, 1, 0, math:sqrt(Num))  triangles(Num + NewSide, NewSide+1);
	false -> Num
    end.