Solving Project Euler #12 with Matlab - algorithm

Question

I am trying to solve Problem #12 of Project Euler with Matlab and this is what I came up with to find the number of divisors of a given number:
function [Divisors] = ND(n)
p = primes(n); %returns a row vector containing all the prime numbers less than or equal to n
i = 1;
count = 0;
Divisors = 1;
while n ~= 1
while rem(n, p(i)) == 0 %rem(a, b) returns the remainder after division of a by b
count = count + 1;
n = n / p(i);
end
Divisors = Divisors * (count + 1);
i = i + 1;
count = 0;
end
end
After this, I created a function to evaluate the number of divisors of the product n * (n + 1) / 2 and when this product achieves a specific limit:
function [solution] = Solution(limit)
n = 1;
product = 0;
while(product < limit)
if rem(n, 2) == 0
product = ND(n / 2) * ND(n + 1);
else
product = ND(n) * ND((n + 1) / 2);
end
n = n + 1;
end
solution = n * (n + 1) / 2;
end
I already know the answer and it's not what comes back from the function Solution. Could someone help me find what's wrong with the coding.
When I run Solution(500) (500 is the limit specified in the problem), I get 76588876, but the correct answer should be:
76576500.

Answer 1

The trick is quite simple while it also bothering me for a while: The iteration in you while loop is misplaced, which would cause the solution a little bigger than the true answer.
function [solution] = Solution(limit)
n = 1;
product = 0;
while(product < limit)
n = n + 1; %%%But Here
if rem(n, 2) == 0
product = ND(n / 2) * ND(n + 1);
else
product = ND(n) * ND((n + 1) / 2);
end
%n = n + 1; %%%Not Here
end
solution = n * (n + 1) / 2;
end
The output of Matlab 2015b:
>> Solution(500)
ans =
76576500