The sequence of triangle numbers is generated by adding the natural numbers. So the 7th 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?

– Project Euler Problem 12

function getNumberOfDivisors(n::UInt64)
        # using sqrt to reduce number of operations by half
        divisors::UInt64 = 0;
        for i in 1:1:(sqrt(n))
                if n%i == 0
                        divisors +=2;
                end
        end
        if sqrt(n)^2 == n
                divisors -=1;
        end     
        return divisors
end




function getNumber(N::UInt64)
        currDivisors::UInt64 = 0;
        currNumber::UInt64 = 0;
        i::UInt64 = 1;
        while currDivisors <= N
                currNumber += i;
                i += 1;
                currDivisors = getNumberOfDivisors(currNumber);
        end     
        return currNumber
end     



function parseARGS()
        if isempty(ARGS)
                numberOfDivisors::UInt64 = 500;
        else    
                numberOfDivisors = tryparse(UInt64,ARGS[1]);
        end     
        return numberOfDivisors
end     

function main()
        numberOfDivisors::UInt64 = parseARGS();
        firstTriangleNumberBelowThreshold = getNumber(numberOfDivisors);
        println(firstTriangleNumberBelowThreshold)
end     

main()


$ julia ProjectEuler0012.jl 5
28
  0.000067 seconds (17 allocations: 912 bytes)

$ julia ProjectEuler0012.jl 10
120
  0.000065 seconds (17 allocations: 912 bytes)
  
$ julia ProjectEuler0012.jl 50
25200
  0.000952 seconds (19 allocations: 944 bytes)

$ julia ProjectEuler0012.jl 100
73920
  0.003015 seconds (19 allocations: 944 bytes)
  
$ julia ProjectEuler0012.jl 250
2162160
  0.085168 seconds (19 allocations: 944 bytes)
  
$ julia ProjectEuler0012.jl 500
76576500
  3.157186 seconds (19 allocations: 944 bytes)

Brute forcing it is too slow! Perhaps there is some clever way to solve this using prime factorization.