Number of combinations as in
A001700.
a(n + 1) / a(n) is fairly large if n + 1 is prime; for the given data, it's at least three. In the other cases it's less than 2.
Let p be a distinct product as described in the name. We look at the factors rather than the result. For n = 4, we see the product p = 1*2*3*3.
Let F(p) be a vector of size n which counts the frequency F_e of each e where 1 <= e <= n. For n = 4 and the product we find (1,1,2,0).
For n = 6, we can put the following restrictions on a vector F(p) = (f_1, f_2, f_3, f_4, f_5, f_6): Trivially, f_e >= 0, f_1+f_2+...+f_6 = 6.
Furthermore,
f_2 * f_3 = 0, as 2*3 = 1*6 and 1<=n=6 and 6<=n=6, so if f_2, f_3 > 0, the value of the product isn't unique, contradiction;
f_2 < 2, 2*2 = 1*4;
f_3 * f_4 = 0 as 3*4 = 2*6. (End)
