That's Halyomorpha Halys. Or the brown marmorated stink bug, to you and me.
Until 1996, they were not native to Pennsylvania -- or the United States, for that matter. Somehow they sneaked in.
If you live in an old house in my neck of the woods, with woods being meant more or less literally, you most likely have run into these fellows. They tend to show up in droves as the weather gets cooler, seeking out warm places to hibernate until spring arrives.
The unnerving sound of their erratic flight, a sudden buzzing that almost always ends with an abrupt thwack, is as common as the sight of them. They don't so much land as crash into things -- walls, furniture, you. Probably the reason one finds a lot of them dead.
Whether dead or alive, be cautious in handling them. Their name is well earned. When threatened (or squashed), or insulted, they emit a very disagreeable odor -- like rancid almonds, I have read. So far I have not experienced this first hand. Having been forewarned, I am careful.
Pick them up in a tissue and flush them down the toilet, is my advice. Rehabilitation -- to borrow from Woody Allen -- is out of the question.