# Better notation for a product

Let $A,B$ are two positive integers. Assuming that we have a product of the form $$\prod_{\substack{a\mid A \\ \gcd(a,B)=1}}f(a).$$ Is there a better notation to be used instead of $a\mid A$ and $\gcd(a,B)=1$ under the product sign Bests

• I would suggest two steps: first define the index set. Quite often that gives profit in the sequel too. – drhab Oct 17 '14 at 9:47
• To flush out what @drhab means: Let $X=\left\{x: x|A \text{ and } \gcd(x,B)=1\right\}$. Then just take the product over all $x\in X$. And it's also pretty common to write $\gcd(x,B)=1$ as just $(x,B)=1$. Usually context implies we mean $\gcd$. – BeaumontTaz Oct 17 '14 at 9:49
• @drhab and BeaumonTaz, thanks for the comments. Indeed I am trying to avoid adding extra definition like a set $X$. But if this is the only possibility then I will do this. – user80225 Oct 17 '14 at 12:55