Find out the largest LCM of the partitions of n I want to find out an algorithm to find out the largest least common multiple (LCM) of the partitions of an integer $n$.

Example:  $5 = 1 + 4$, $5 = 2 + 3$, since $\mathrm{LCM}(1,4) &lt; \mathrm{LCM}(2,3) = 6$, the largest LCM of the partitions of $5$ is 6.

The definition of "partition" is the standard definition of it. In order to make the problem more clearly, I will take n = 10 as an example. The largest LCM if the partitions of 10 is 30, since 10 = 2 + 3 + 5.
More examples(Let g(n) be the answer that I want to get):
g(11) = 30
g(12) = 60
g(13) = 60

I want to find out an algorithm that can get the largest LCM in 1 second with the n less or equal to 250.
It seems that this a competition problem. Your best bet is to pre-calculate maximum values for all numbers(250 isn't very big) and store it into an array. That would be the best bet as this can give you timing near to zero.