Is it farther or further?
c.1600, "cheating;" present participle adjective from amuse (v.). Sense of "interesting" is from 1712; that of "pleasantly entertaining, tickling to the fancy" is from 1826. Noted late 1920s as a vogue word. Amusive has been tried in all senses since 18c. and might be useful, but it never caught on. Related: Amusingly.
late 15c., "to divert the attention, beguile, delude," from Middle French amuser "divert, cause to muse," from a "at, to" (but here probably a causal prefix) + muser "ponder, stare fixedly" (see muse (v.)). Sense of "divert from serious business, tickle the fancy of" is recorded from 1630s, but through 18c. the primary meaning was "deceive, cheat" by first occupying the attention. Bemuse retains more of the original meaning. Related: Amused; amusing.