(n, n+1) Higher Sum and Product

Among the distinct pairs of numbers whose sum is   $n = 2a$ ,
the greatest possible product is   $n^2$

Consider   $n+1$ ,   find the distinct ways of achieving a higher product with two positive integers

Here are the first few examples:

If we want   $n+1$   to achieve 10 distinct ways a higher product with two positive integers, what should be   $n$ ?
Find the smallest   $n$