Goodwill and Acquired Intangibles (Details 2) - USD ($) $ in Thousands	12 Months Ended
Dec. 31, 2022	Jan. 01, 2022	Jan. 02, 2021
Amortization of acquired intangibles
Cost of product and maintenance	$ 41,348	$ 47,576	$ 46,184
Amortization of acquired intangibles	18,470	19,640	18,009
Total amortization of acquired intangibles	$ 59,818	$ 67,216	$ 64,193

The aggregate expense charged against earnings to allocate the cost of intangible assets (nonphysical assets not used in production) in a systematic and rational manner to the periods expected to benefit from such assets. As a noncash expense, this element is added back to net income when calculating cash provided by or used in operations using the indirect method.

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
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Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
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Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
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