At least part of the problem has nothing to do with subclassing from int and instead is related to pickling objects with circular references.

I am attaching a patch that demonstrates the problem.  In issue1581183-test.diff, I modified memoize so that it does nothing rather than fails an assert if object is already in the memo.  This makes python and C implementations behave the same, but still fail to produce correct results. Pickling with protocol 2 break circular reference and instead creates two independent objects.