Using Java singleton pattern (static access to the singleton) with Spring

Consider this code:

public class A {
    private static final A INSTANCE = new A();
    public A getInstance() {
        return INSTANCE;
    }
    private A() {}
    public void doSomething() {}
}

// elsewhere in code
A.getInstance().doSomething();

How do I do the same when A requires a spring bean for construction? I don't want to inject A in each class that needs it, but want those classes to be able to access the singleton instance statically (ie, A.getInstance()).