While looking into ways of generating certain kinds of pseudo-random number sequences I came up with the issue of finding the maximum of products of distict primes with a sum less than N. I'm wondering if this sequence has a name.
This is what I think the start of the sequence looks like :
N : p_i : Product
2 : 2 : 2
3 : 3 : 3
4 : 3 : 3
5 : 2,3 : 6
6 : 2,3 : 6
7 : 2,5 : 10
8 : 3,5 : 15
9 : 3,5 : 15
10 : 2,3,5 : 30
11 : 2,3,5 : 30
12 : 2,3,7 : 42
Aside: This came up in generating random numbers using the following algorithm
$$ r_i = v_1[i\;\textrm{mod}\;p_1] \;\textrm{xor}\; v_2[i\;\textrm{mod}\;p_2] \;\textrm{xor}\; v_3[i\;\textrm{mod}\;p_3] \ldots $$
which has the nice property that you can get to $r_i$ without calculating $r_{i-1}$, and is fast, but is otherwise a very weak PRNG. The cycle length of the generator is given by the product of the primes, and the space taken up by the tables of $v_k$ is the sum of their sizes. Thus the function above gives the maximum cycle length for a given table size.
