하염하염없이 is translated by naver dic as blankly, vacantly:
그는 하염없이 벽만 바라보았다 - He stared blankly at the wall.
하염없이 걷다 - walk endlessly
A formation of X-없이 would normally suggest that X would be a noun with some particular meaning, but there doesn't seem to be such a thing as a '하염'. Was there ever? if not, what's the origin of the word 하염없이?