Goodwill and Acquired Intangibles (Details 1) - USD ($) $ in Thousands	Oct. 02, 2021	Jan. 02, 2021
Acquired intangibles with finite lives, excluding intangibles fully amortized at end of prior fiscal year
Gross carrying amount	$ 618,835	$ 561,451
Accumulated amortization	(371,207)	(350,861)
Total estimated amortization expense	247,628	210,590
Existing Technology [Member]
Acquired intangibles with finite lives, excluding intangibles fully amortized at end of prior fiscal year
Gross carrying amount	402,640	370,838
Accumulated amortization	(242,829)	(230,654)
Total estimated amortization expense	159,811	140,184
Agreements and Relationships [Member]
Acquired intangibles with finite lives, excluding intangibles fully amortized at end of prior fiscal year
Gross carrying amount	205,454	180,023
Accumulated amortization	(125,436)	(113,629)
Total estimated amortization expense	80,018	66,394
Tradenames Trademarks And Patents [Member]
Acquired intangibles with finite lives, excluding intangibles fully amortized at end of prior fiscal year
Gross carrying amount	10,741	10,590
Accumulated amortization	(2,942)	(6,578)
Total estimated amortization expense	$ 7,799	$ 4,012