Goodwill and Acquired Intangibles (Details 1) - USD ($) $ in Thousands	Dec. 31, 2022	Jan. 01, 2022
Acquired intangibles with finite lives, excluding intangibles fully amortized at end of prior fiscal year
Gross carrying amount	$ 767,399
Accumulated amortization	(419,582)	$ (387,939)
Acquired intangibles, net	347,817
In-process technology	6,800
Intangible Assets, Gross (Excluding Goodwill)	774,199	621,204
Intangible Assets, Net (Excluding Goodwill)	354,617	233,265
Existing technology [Member]
Acquired intangibles with finite lives, excluding intangibles fully amortized at end of prior fiscal year
Gross carrying amount	479,796	405,481
Accumulated amortization	(278,851)	(254,599)
Acquired intangibles, net	200,945	150,882
Agreements and relationships [Member]
Acquired intangibles with finite lives, excluding intangibles fully amortized at end of prior fiscal year
Gross carrying amount	274,624	205,057
Accumulated amortization	(137,847)	(130,187)
Acquired intangibles, net	136,777	74,870
Tradenames, trademarks and patents [Member]
Acquired intangibles with finite lives, excluding intangibles fully amortized at end of prior fiscal year
Gross carrying amount	12,979	10,666
Accumulated amortization	(2,884)	(3,153)
Acquired intangibles, net	$ 10,095	$ 7,513

Accumulated amount of amortization of assets, excluding financial assets and goodwill, lacking physical substance with a finite life.

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 350
-SubTopic 30
-Section 50
-Paragraph 2
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-URI https://asc.fasb.org/extlink&oid=66006027&loc=d3e16323-109275

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
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Amount before amortization of assets, excluding financial assets and goodwill, lacking physical substance with a finite life.

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-Publisher FASB
-Name Accounting Standards Codification
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