Some dogs are instant buddies, others are not. A month is a very short time for those who are not. There is no guarantee that they will ever entertain each other the way we would all love to see dogs get along, but I think even when they appear to ignore each other, they appreciate having another dog around.
When I brought my second dog home, the boys got along but we had jealousy issues to work through. Some of the problems were solved within a couple days, others took a couple weeks, and the last ones took a couple of months. My boys still compete for attention and have little jealous moments. It's a bit of a balancing act making sure each one gets what he needs.
Be patient and consistent and let the dogs grow together on their own terms. Walking together and encouraging playing together is great. My boys play together, but they want me involved. They don't self entertain.
Little stinkers.