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Goodwill and Acquired Intangibles (Details 1) - USD ($) $ in Thousands | Jan. 02, 2021 | Dec. 28, 2019
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Acquired intangibles with finite lives, excluding intangibles fully amortized at end of prior fiscal year |  |
Gross carrying amount | $ 561,451 | $ 517,137
Accumulated amortization | (350,861) | (364,262)
Acquired intangibles, net | 210,590 | 152,875
In-process technology |  | 19,500
Intangible Assets, Gross (Excluding Goodwill) |  | 536,637
Intangible Assets, Net (Excluding Goodwill) | 210,590 | 172,375
Existing technology [Member] |  |
Acquired intangibles with finite lives, excluding intangibles fully amortized at end of prior fiscal year |  |
Gross carrying amount | 370,838 | 363,142
Accumulated amortization | (230,654) | (245,902)
Acquired intangibles, net | 140,184 | 117,240
Agreements and relationships [Member] |  |
Acquired intangibles with finite lives, excluding intangibles fully amortized at end of prior fiscal year |  |
Gross carrying amount | 180,023 | 146,395
Accumulated amortization | (113,629) | (112,565)
Acquired intangibles, net | 66,394 | 33,830
Tradenames, trademarks and patents [Member] |  |
Acquired intangibles with finite lives, excluding intangibles fully amortized at end of prior fiscal year |  |
Gross carrying amount | 10,590 | 7,600
Accumulated amortization | (6,578) | (5,795)
Acquired intangibles, net | $ 4,012 | $ 1,805

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