Background Let \$a\$ \$\in \mathbb{N}\$ and \$b\$ \$\in \mathbb{N}\$ and \$S\$ be some set of Naturals. Consider \$X(a ,b, S)\$: The number of integer partitions of \$a\$ into \$b\$ many parts, where each of the \$b\$ numbers are co-prime to all elements of \$S\$. Example: $$X(a ,2, \{a\}) = |\{(x, y): x + y = a,\ gcd(a, x) = gcd(a, y) = 1,\ x \leq\ y\}|$$ In fact it can be sh…