Goodwill and Acquired Intangibles (Details 1) - USD ($) $ in Thousands	Apr. 03, 2021	Jan. 02, 2021
Acquired intangibles with finite lives, excluding intangibles fully amortized at end of prior fiscal year
Gross carrying amount	$ 601,862	$ 561,451
Accumulated amortization	(337,191)	(350,861)
Total estimated amortization expense	264,671	210,590
Existing Technology [Member]
Acquired intangibles with finite lives, excluding intangibles fully amortized at end of prior fiscal year
Gross carrying amount	393,026	370,838
Accumulated amortization	(219,061)	(230,654)
Total estimated amortization expense	173,965	140,184
Agreements and Relationships [Member]
Acquired intangibles with finite lives, excluding intangibles fully amortized at end of prior fiscal year
Gross carrying amount	198,546	180,023
Accumulated amortization	(115,650)	(113,629)
Total estimated amortization expense	82,896	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	10,290	10,590
Accumulated amortization	(2,480)	(6,578)
Total estimated amortization expense	$ 7,810	$ 4,012