Touch lamp turns on and off with fan switches in the house
I have a floor standing touch lamp in our living room that has a three way bulb and you "touch" the metal to turn it on and off. We've noticed a couple times a week that the action of switching on and off a switch, almost always a fan switch, will "click" the lamp like it's being touched. The lamp goes off - 50w - 100w - 150 w so if its at 150w and this happens it turns off. If its off and this happens it goes to 50w, etc. We've noticed 90% of the time it's doing this is when our half bath exhaust fan is turned on or off or our bedroom ceiling fan is turned on or off (or between speeds). I thought at first that there all on the same circuit but they are not. The other night when we switched our fan in the bedroom on we saw the light turn on. We rotated our speed switch a couple times back and forth and the light went through it's cycle back to off. A little creepy.
What would cause this and is there anything that can be done to fix it? The lamp is a standard two prong without ground. I mean I could just get another lamp but it worries me that it does it in the first place.