Easton's 1897 Bible Dictionary:

Ahimelech
   brother of the king, the son of Ahitub and father of Abiathar (1
   Sam. 22:20-23). He descended from Eli in the line of Ithamar. In
   1 Chr. 18:16 he is called Abimelech, and is probably the same as
   Ahiah (1 Sam. 14:3, 18). He was the twelfth high priest, and
   officiated at Nob, where he was visited by David (to whom and
   his companions he gave five loaves of the showbread) when he
   fled from Saul (1 Sam. 21:1-9). He was summoned into Saul's
   presence, and accused, on the information of Doeg the Edomite,
   of disloyalty because of his kindness to David; whereupon the
   king commanded that he, with the other priests who stood beside
   him (86 in all), should be put to death. This sentence was
   carried into execution by Doeg in the most cruel manner (1 Sam.
   22:9-23). Possibly Abiathar had a son also called Ahimelech, or
   the two names, as some think, may have been accidentally
   transposed in 2 Sam. 8:17; 1 Chr. 18:16, marg.; 24:3, 6, 31.


Hitchcock's Bible Names Dictionary (late 1800's):

Ahimelech, my brother is a king; my king's brother