A109510 Values of n such that sigma(n)-2n (the abundance of n) is a (positive) square.

6, 12, 28, 70, 88, 108, 168, 220, 348, 496, 550, 580, 726, 748, 798, 910, 918, 952, 1032, 1120, 1200, 1240, 1504, 1644, 1672, 1840, 1888, 2140, 2205, 2392, 2470, 2472, 2814, 3190, 3222, 3580, 3804, 4030, 4648, 4732, 4758, 5032, 5670, 5830