Changes in Accounting Policies (Details) - USD ($) $ in Thousands	3 Months Ended									12 Months Ended
	Jan. 03, 2021		Oct. 04, 2020	Jul. 05, 2020	Apr. 05, 2020	Dec. 29, 2019	Sep. 29, 2019	Jun. 30, 2019	Mar. 31, 2019	Jan. 03, 2021	Dec. 29, 2019	Dec. 30, 2018	Dec. 31, 2017
Revenue, Initial Application Period Cumulative Effect Transition [Line Items]
Revenue from Contract with Customer, Excluding Assessed Tax										$ (3,782,745)	$ (2,883,673)	$ (2,777,996)
Selling, general and administrative expenses										917,894	815,318	811,913
Research and development expenses										205,389	189,336	193,998
Restructuring and other costs, net	$ (3,062)		$ 4,059	$ 1,158	$ 5,858	$ 1,560	$ 14,068	$ 6,161	$ 7,639	8,013	29,428	11,144
Interest and other expense, net										72,217	124,831	66,201
Restructuring and contract termination charges, net										(8,013)	(29,428)	(11,144)
Operating income from continuing operations	510,254	[1]	248,006	175,639	44,682	138,248	78,660	91,735	53,330	978,581	361,973	323,884
Nonoperating Income (Expense)										72,217	124,831	66,201
Income (Loss) from Continuing Operations before Equity Method Investments, Income Taxes, Noncontrolling Interest	473,091	[1]	233,757	164,827	34,689	65,296	63,254	71,827	36,765	906,364	237,142	257,683
Provision for income taxes										178,266	9,389	20,208
Operating income from continuing operations	380,434	[1]	176,736	137,213	33,715	64,549	58,610	69,141	35,453	728,098	227,753	237,475
(Loss) gain on disposition of discontinued operations before income taxes										(76)	0	(859)
Cash and cash equivalents	402,036					191,877				402,036	191,877	163,111
Accounts receivable, net	(1,155,109)					(725,184)				(1,155,109)	(725,184)
Inventories	514,567					356,937				514,567	356,937
Other current assets	(167,208)					(100,381)				(167,208)	(100,381)
Property, plant and equipment, net	368,304					318,223				368,304	318,223
Intangible assets, net	1,365,693					1,283,286				1,365,693	1,283,286
Goodwill	3,447,114					3,111,227				3,447,114	3,111,227	2,952,608
Other assets, net	333,048					284,173				333,048	284,173
Current portion of long-term debt	380,948					9,974				380,948	9,974
Assets	(7,960,315)					(6,538,564)				(7,960,315)	(6,538,564)
Accounts payable	327,325					235,855				327,325	235,855
Accrued restructuring and contract termination costs	4,716					11,559				4,716	11,559
Accrued expenses and other current liabilities	937,027					503,332				937,027	503,332
Current liabilities of discontinued operations	2,173					2,112				2,173	2,112
Long-term debt	1,609,701					2,064,041				1,609,701	2,064,041
Long-term liabilities	774,531					751,468				774,531	751,468
Liabilities	4,224,823					3,724,740				4,224,823	3,724,740
Preferred stock—$1 par value per share, authorized 1,000,000 shares; none issued or outstanding	0					0				0	0
Common Stock, Value, Issued	112,090					111,140				112,090	111,140
Capital in excess of par value	148,101					90,357				148,101	90,357
Retained earnings	3,507,262					2,811,973				3,507,262	2,811,973
Accumulated other comprehensive loss	(31,961)					(199,646)				(31,961)	(199,646)	(176,481)	$ (46,518)
Stockholders' Equity Attributable to Parent	3,735,492					2,813,824				3,735,492	2,813,824	2,584,955	$ 2,503,188
Liabilities and Equity	(7,960,315)					(6,538,564)				(7,960,315)	(6,538,564)
Net income	380,361	[1]	176,699	137,162	33,665	64,501	58,558	69,087	35,412	727,887	227,558	237,927
Provision For Income Taxes On Discontinued Operations And Dispositions										135	(195)	1,311
Income (Loss) from Discontinued Operations, Net of Tax, Attributable to Parent	$ (73)		$ (37)	$ (51)	$ (50)	$ (48)	$ (52)	$ (54)	$ (41)	(211)	(195)	452
Product [Member]
Revenue, Initial Application Period Cumulative Effect Transition [Line Items]
Revenue from Contract with Customer, Excluding Assessed Tax										(2,778,725)	(2,017,042)	(1,935,493)
Cost of Goods and Services Sold										(1,105,614)	(956,398)	(908,228)
Service [Member]
Revenue, Initial Application Period Cumulative Effect Transition [Line Items]
Revenue from Contract with Customer, Excluding Assessed Tax										(1,004,020)	(866,631)	(842,503)
Cost of Goods and Services Sold										$ (567,254)	$ (531,220)	$ (528,829)

[1] The fourth quarter of fiscal year 2020 includes a pre-tax loss of $25.4 million as a result of the mark-to-market adjustment on postretirement benefit plans. The fourth quarter of fiscal year 2019 includes a pre-tax loss of $31.2 million as a result of the mark-to-market adjustment on postretirement benefit plans. See Note 1 for a discussion of this accounting policy