B737 ACFT. AFTER TKOF; THE FLC WAS UNABLE TO RAISE THE LNDG GEAR. CHKLISTS WERE COMPLETED; COMPANY NOTIFIED; AND DECISION WAS MADE TO RETURN AND LAND. FLC WAS VECTORED IMMEDIATELY BACK TO THE ILS; A DISCRETE TWR FREQ WAS ASSIGNED. FLC VERY BUSY LOADING IN NEW APCH INTO FMC; CHKLISTS; ETC; AND FORGOT TO OBTAIN LNDG CLRNC FROM TWR. WERE ADVISED AFTER LNDG.

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WE DEPARTED SEA IN A B737 AND THE GEAR WOULD NOT RETRACT. WE ACCOMPLISHED THE 'AFTER TKOF' CHKLIST AND BEGAN THE 'LNDG GEAR WILL NOT COME UP' CHKLIST WHICH RECOMMENDS TO LAND. THE COMPANY MAINT ALSO SUGGESTED WE RETURN. WE LEVELED OFF AT 5000 FT AND ASKED DEP CTL FOR CLRNC TO RETURN AND DESCRIBED THE PROB TO THEM. WE MADE A QUICK RETURN TO THE ILS AND WERE CLRED FOR THE ILS RWY 16R AND TOLD TO CONTACT THE TWR ON AN UNUSUAL FREQ AT THE OM. IN THE MEANTIME; WE HAD TO BUILD THE APCH IN THE FMS AND CHANGE DEST AND CRUISE ALT. WE ALSO (ON FINAL APCH) REMEMBERED TO DISCUSS AN OVERWT LNDG; USE MAX FLAPS AND LAND SMOOTHLY. WE HAD A JUMPSEAT RIDER WHO WAS MONITORING ATC FREQ. ON FINAL WE HAD TO COMPLETE THE GEAR ABNORMAL DSCNT AND APCH CHKS WITH THE GEAR HORN BLARING. I FAILED TO CONTACT TWR AND WE LANDED WITHOUT A CLRNC. NEITHER OF THE OTHER 2 PLTS CAUGHT IT EITHER. ON ROLLOUT I CONTACTED THE TWR. WE HAD FIRE TRUCKS FOLLOW US TO THE GATE; DUE TO THE GEAR MALFUNCTION. I AM AN INSTRUCTOR CAPT; AND CANNOT BELIEVE THAT I COULD FAIL AT THIS MOST BASIC RULE. THIS WILL CERTAINLY NOT HAPPEN AGAIN. I HAVE AN ACTUAL SCENARIO TO USE WITH MY STUDENTS IN THE SIMULATOR NOW.