How should I store a list of weak pointers in the factory class?

There is a Factory class in my project, which returns std::shared_ptr<MyClass>, if the Create method is called. The factory is not the owner, but it maintains a list of created objects. Sometimes the factory needs to iterate over the created objects which are still used, or count them.

I implemented this using std::vector<std::weak_ptr<MyClass>>. The iteration looks like this:

for (std::weak_ptr<MyClass> wp : weak_list) {
    if (auto sp = wp.lock()) {
        //..
    }
}

The Create function:

std::shared_ptr<MyClass> Create(/* ... */) {
    std::shared_ptr<MyClass> obj = std::make_shared<MyClass>();

    //...

    weak_list.push_back(obj);
    return obj;
}

Is vector the best container for a list like this? Maybe std::set would be better.

If I implement this using a vector, I have to check regularly for expired pointers in the list and remove them

What is the preferred way to store a list of weak pointers in the factory class?