Stock Compensation Plans and Stock Based Compensation (Details 1) - USD ($) $ in Thousands	12 Months Ended
	Jan. 02, 2021	Dec. 28, 2019	Dec. 29, 2018
Stock based compensation expense and allocation by cost
Stock-based compensation	$ 197,268	$ 181,547	$ 167,715
Cost of product and maintenance [Member]
Stock based compensation expense and allocation by cost
Stock-based compensation	2,922	2,759	2,631
Cost of services [Member]
Stock based compensation expense and allocation by cost
Stock-based compensation	3,720	3,510	3,714
Marketing and sales [Member]
Stock based compensation expense and allocation by cost
Stock-based compensation	42,096	39,088	34,665
Research and development [Member]
Stock based compensation expense and allocation by cost
Stock-based compensation	124,999	114,656	104,353
General and administrative [Member]
Stock based compensation expense and allocation by cost
Stock-based compensation	$ 23,531	$ 21,534	$ 22,352