CTLR FAILED TO ISSUE DEP HEADING AND ALT.

Narrative

THE GORMAN 1 DEP SID FROM LAX SPECIFIES 250 DEG HDG AND MAINTAIN 2000 FT MSL FOR RADAR VECTORS. MANY TIMES THE TWR INSTRUCTS DEPARTING ACFT TO FLY HEADING 270 DEGS AND MAINTAIN 3000 FT AS THEY CLR YOU FOR TKOF. THE TWR CTLR WAS EXTREMELY BUSY AND CLRED THE ACFT IN FRONT OF US FOR 270 DEGS PLUS 3000 FT. WE WERE THEN CLRED INTO POS AND HOLD. WE WERE TOLD TO 'RPT THE DEPARTING ACFT IN SIGHT AND MAINTAIN VISUAL SEPARATION WITH HIM' AND THEN CLRED FOR TKOF. WE ACKNOWLEDGED AND TOOK OFF. WE TOOK OFF AND FLEW THE SID 258 DEGS AND 2000 FT. WE ASKED THE CTLR IF HE WANTED US OVER THE DEP BECAUSE HE FORGOT TO SWITCH US DUE TO BEING BUSY. HE SAID 'OH YES CONTACT DEP.' A B737 WAS CLRED FOR TKOF RIGHT BEHIND US AND NOT GIVEN A TURN. HE WAS TOLD TO MAINTAIN VISUAL WITH US. THE DEP CTLR SAID THE TWR CTLR TOLD HIM THAT HE TOLD US TO TURN TO 270 DEGS AFTER TKOF AND DID WE NOT HEAR HIM. WE SAID HE DID NOT GIVE US ANY SPECIAL INSTRUCTIONS. THE DEP CTLR SAID 'I BELIEVE YOU; THIS IS THE THIRD TIME THIS HAS HAPPENED.' I BELIEVE THAT MAY BE WHAT THE TWR CTLR WAS THINKING BUT DUE TO HIS WORKLOAD HE DID NOT VERBALIZE IT. THIS SEEMED TO BE CONFIRMED BY THE DEP CTLR'S STATEMENT.