Goodwill and Acquired Intangibles (Details 1) - USD ($) $ in Thousands	Jan. 01, 2022	Jan. 02, 2021
Acquired intangibles with finite lives, excluding intangibles fully amortized at end of prior fiscal year
Accumulated amortization	$ (387,939)	$ (350,861)
Acquired intangibles, net	233,265
Intangible Assets, Gross (Excluding Goodwill)	621,204	561,451
Intangible Assets, Net (Excluding Goodwill)	233,265	210,590
Existing technology [Member]
Acquired intangibles with finite lives, excluding intangibles fully amortized at end of prior fiscal year
Gross carrying amount	405,481	370,838
Accumulated amortization	(254,599)	(230,654)
Acquired intangibles, net	150,882	140,184
Agreements and relationships [Member]
Acquired intangibles with finite lives, excluding intangibles fully amortized at end of prior fiscal year
Gross carrying amount	205,057	180,023
Accumulated amortization	(130,187)	(113,629)
Acquired intangibles, net	74,870	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	10,666	10,590
Accumulated amortization	(3,153)	(6,578)
Acquired intangibles, net	$ 7,513	$ 4,012

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
-Subparagraph (a)(1)
-URI http://asc.fasb.org/extlink&oid=66006027&loc=d3e16323-109275

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

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 928
-SubTopic 340
-Section 50
-Paragraph 1
-URI http://asc.fasb.org/extlink&oid=6473545&loc=d3e61844-108004

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

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Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
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-SubTopic 20
-Section 50
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-URI http://asc.fasb.org/extlink&oid=120154696&loc=d3e54445-107959

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