EMB190 Captain (PF) reports failing to retract the landing gear after takeoff due to distractions (ATC call and EICAS messages). The gear noise is heard but not correlated with the gear being down. A decision is made to divert when the FMC indicates insufficient fuel and the gear is discovered to be down during the return.

Narrative

The flight started with an hour ground delay for ZZZ1 ground stop. After the ground stop was lifted; we started the APU. I checked the fuel on board and we had 8440 pounds of fuel on board. It was a quick taxi out so we would burn less than 200 pounds. Minimum fuel on take off was 6829 pounds. Upon take off the First Officer stated positive rate and I said gear up; at this time tower called for a frequency change. The First Officer answered the call switched frequency and contacted departure. At this time we had three EICAS messages and then they went away. I believe one was Nav/Radio 1 & 2 off; but I don't recall the other two. We retracted the flaps and I called for the after take off check list. At this time we got a check reserve fuel message on the FMS; and the First Officer mentioned about it being noisy on the flight deck. The clearance was to fly the departure to 9000 feet. The departure required full attention due to the terrain; cloud coverage on top of the mountain; and the three turns we had to make prior to the VOR; so we had the terrain map up for situational awareness. I was aware of the noise and at 900 feet started to check each system for abnormality. At this time I believe the First Officer was checking the FMS for accuracy and to see if our fixes were valid. At the VOR we were given direct and assigned a higher altitude. We started a climb but then informed ATC we need to level off but I'm nor sure which altitude we we stopped at. The noise was loud at this point and we had an indication on the FMS that we would land at destination with 800 pounds. We decided to divert and have maintenance check it out. I didn't fly faster than 240 knots thinking it may be structural damage or a fuel leak. After getting clearance; we went through the systems and previous procedures and discovered that the landing gear was still down. We retracted the gear after slowing down and then recalculated the required fuel to destination. We had 5500 pounds at that time and that was not enough with the required reserve of 2800 pounds. We then requested a change of destination back to the departure airport since it was closer and it would accommodate the passengers better. We were vectored around and landed safely. We talked to dispatch and got more fuel and a new release. After about an hour we took off. Do not to get distracted by radio calls; or aircraft messages. Make sure the items on the checklist are performed; and if some thing feels wrong; go back and rerun the previous check lists and physically touch each control on the check list and make sure it was performed. Always make sure the other pilot is actually doing the actions on the checklist.