Goodwill and Acquired Intangibles (Details 2) - USD ($) $ in Thousands	3 Months Ended	9 Months Ended
Sep. 30, 2023	Oct. 01, 2022	Sep. 30, 2023	Oct. 01, 2022
Amortization of acquired intangibles
Cost of product and maintenance	$ 10,991	$ 8,867	$ 31,869	$ 30,906
Amortization of acquired intangibles	4,612	3,946	13,181	13,543
Total amortization of acquired intangibles	$ 15,603	$ 12,813	$ 45,050	$ 44,449

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
-Name Accounting Standards Codification
-Section 45
-Paragraph 28
-Subparagraph (b)
-SubTopic 10
-Topic 230
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482740/230-10-45-28

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Topic 350
-SubTopic 30
-Section 45
-Paragraph 2
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482686/350-30-45-2

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Topic 350
-SubTopic 30
-Section 50
-Paragraph 2
-Subparagraph (a)(2)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482665/350-30-50-2

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