IA 1125 CREW EXPERIENCES ENG ICING CLBING TO FL410 WHICH INITIALLY GOES UNDETECTED AND CAUSES PWR DEFICIT.

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DURING CLB TO FL410; I NOTICED THE TGT WAS LOWER THAN NORMAL AND THAT I HAD TO KEEP DECREASING THE CLB RATE. THE MACH NUMBER CONTINUED TO DECREASE EVEN WITH THE DECREASED RATE OF CLB. I HAD THE THROTTLE FULL FORWARD AND WAS ONLY GETTING 770 DEGS C. USUALLY GET ABOUT 900 DEGS. I HAD TO LEVEL AT FL405; BUT WHEN I LEVELED OFF I STARTED TO GET A SLIGHT VIBRATION AND THE ANGLE OF ATTACK INDICATOR WAS OUT OF THE GREEN AND AT THE EDGE OF THE YELLOW ARC. TOLD THE COPLT TO REQUEST LOWER AND EASED THE NOSE OVER SLIGHTLY INTENDING TO MAINTAIN FL400. THE CTLR SAID HE WAS UNABLE TO GIVE US LOWER DUE TO TFC. I ASKED FOR A VECTOR TO GET LOWER AND WAS TOLD UNABLE. AT FL400 THE BUFFET CONTINUED AND I DECLARED AN EMER. THE CTLR CLRED US TO FL360 THEN LATER ASKED IF WE COULD MAINTAIN FL370; CORRECT FOR DIRECTION OF FLT. WE WERE ABLE TO MAINTAIN FL370; WHEN LEVEL I APPLIED ENG ANTI-ICE AND THE ENG REGAINED FULL PWR. WHEN HANDED OFF TO THE NEXT CTLR; WE CLBED TO FL410 NORMALLY. THERE WERE SHOWERS AND CLOUDS IN THE AREA; BUT I DID NOT NOTICE ANY ICE ON THE WINDSHIELD OR BOOTS DURING CLB SO ENG ANTI-ICE WAS NOT USED. USE OF ENG ANTI-ICE IN THE CLOUDS WOULD PROBABLY HAVE PREVENTED THIS PROB. I WILL BE USING ENG ANTI-ICE IN THE FUTURE EVEN IF NO OTHER ICING IS APPARENT.