Michael Jordan had the most games by a player 34 or older with 40+ points, with 20 games.

Interpreted as:

most 40 or more point regular-season games after turning 34 years old by a player

	NAME	GP	PTS	MPG	PPG	RPG	APG	SPG	BPG	FGM	FGA	FG%	3PM	3PA	3P%	FTM	FTA	FT%	TS%	OREB	DREB	TPG	MIN	REB	AST	STL	BLK	TOV	PF	+/-
1	Michael Jordan M. Jordan	20	867	41.6	43.4	5.9	3.5	2.1	0.5	16.5	30.3	54.5	0.7	1.8	36.1	9.7	11.5	84.7	61.4	1.5	4.4	1.8	831	118	70	41	10	36	43	+199
2	Stephen Curry S. Curry	17	777	36.1	45.7	5.3	5.2	1.1	0.3	15.7	26.3	59.7	8.3	15.2	54.4	6.0	6.5	91.9	78.4	0.5	4.8	3.0	613	90	89	19	5	51	32	+89
3	LeBron James L. James	15	662	36.9	44.1	9.3	6.5	0.9	0.9	15.9	25.5	62.6	5.3	9.1	58.8	6.9	8.1	85.2	76.0	1.2	8.1	3.5	554	140	97	13	14	52	14	+144
4	Kevin Durant K. Durant	10	426	38.3	42.6	6.1	5.2	1.1	1.4	16.1	26.1	61.7	3.5	7.3	47.9	6.9	7.4	93.2	72.6	0.6	5.5	4.3	383	61	52	11	14	43	24	+27
5	Kobe Bryant K. Bryant	10	436	41.4	43.6	6.2	5.2	1.4	0.9	14.6	28.0	52.1	3.4	9.0	37.8	11.0	12.9	85.3	64.7	0.7	5.5	4.8	414	62	52	14	9	48	15	-27
6	Bernard King B. King	9	419	43.1	46.6	7.4	4.4	2.1	0.3	18.1	32.2	56.2	0.3	1.1	30.0	10.0	11.8	84.9	62.2	2.7	4.8	3.9	388	67	40	19	3	35	28
7	Karl Malone K. Malone	7	303	40.1	43.3	11.3	3.9	1.9	1.9	14.6	23.9	61.1	0.1	0.1	100.0	14.0	17.1	81.7	68.9	1.7	9.6	4.3	281	79	27	13	13	30	23	+53
8	Kareem Abdul-Jabbar K. Abdul-Jabbar	5	210	41.4	42.0	9.6	3.4		2.4	17.0	26.4	64.4	0.0	0.0		8.0	10.0	80.0	68.2				207	48	17		12		13
9	James Harden J. Harden	4	174	34.1	43.5	3.5	6.8	1.5	0.5	12.5	21.8	57.5	6.0	11.3	53.3	12.5	14.3	87.7	77.6	0.5	3.0	3.5	137	14	27	6	2	14	6	+77
10	Alex English A. English	4	176	44.0	44.0	4.3	5.0	1.3	0.0	18.8	31.0	60.5	0.0	0.0		6.5	7.0	92.9	64.6	2.0	2.3	2.3	176	17	20	5	0	9	10
11	Elgin Baylor E. Baylor	4	166	44.8	41.5	12.3	4.3			17.3	28.5	60.5				7.0	9.0	77.8	63.9				179	49	17				15
12	DeMar DeRozan D. DeRozan	3	129	41.5	43.0	6.0	5.7	0.7	0.3	14.7	25.3	57.9	2.7	6.0	44.4	11.0	12.3	89.2	69.9	0.0	6.0	1.7	125	18	17	2	1	5	8	+45
13	Hakeem Olajuwon H. Olajuwon	3	134	42.7	44.7	12.0	4.3	0.7	2.0	17.3	31.0	55.9	0.7	0.7	100.0	9.3	10.3	90.3	62.8	2.3	9.7	4.0	128	36	13	2	6	12	8	+18
14	Damian Lillard D. Lillard	2	84	41.2	42.0	5.5	8.5	1.0	0.5	13.5	25.5	52.9	9.0	15.0	60.0	6.0	7.5	80.0	72.9	0.5	5.0	2.5	82	11	17	2	1	5	5	+6
15	Dirk Nowitzki D. Nowitzki	2	80	36.3	40.0	6.0	4.0	2.0	0.0	13.0	23.0	56.5	4.0	7.0	57.1	10.0	10.5	95.2	72.4	0.0	6.0	1.5	73	12	8	4	0	3	7	+18
16	Paul Pierce P. Pierce	2	83	38.4	41.5	5.0	4.0	2.5	0.5	12.0	17.5	68.6	5.0	6.5	76.9	12.5	13.0	96.2	89.4	0.0	5.0	2.0	77	10	8	5	1	4	6	+31
17	Dominique Wilkins D. Wilkins	2	85	40.5	42.5	10.0	2.0	0.5	1.0	16.0	28.5	56.1	3.5	4.5	77.8	7.0	9.5	73.7	65.0	5.5	4.5	4.5	81	20	4	1	2	9	6
18	Elvin Hayes E. Hayes	2	85	43.5	42.5	11.5	2.0			17.5	26.0	67.3	0.0			7.5	9.0	83.3	70.9				87	23	4				4
19	Richie Guerin R. Guerin	2	82	41.0	41.0	1.5	5.0			16.0	21.0	76.2				9.0	12.0	75.0	78.0				82	3	10				9
20	Nikola Vučević N. Vučević	1	40	34.2	40.0	13.0	3.0	1.0	0.0	17.0	25.0	68.0	2.0	6.0	33.3	4.0	4.0	100.0	74.7	2.0	11.0	0.0	34	13	3	1	0	0	3	+5
21	LaMarcus Aldridge L. Aldridge	1	40	31.8	40.0	9.0	5.0	0.0	3.0	17.0	25.0	68.0	3.0	5.0	60.0	3.0	4.0	75.0	74.7	3.0	6.0	1.0	32	9	5	0	3	1	1	+29
22	Jamal Crawford J. Crawford	1	51	38.1	51.0	5.0	5.0	1.0	1.0	18.0	30.0	60.0	7.0	13.0	53.8	8.0	9.0	88.9	75.1	0.0	5.0	4.0	38	5	5	1	1	4	4	-5
23	Pau Gasol P. Gasol	1	46	38.6	46.0	18.0	3.0	1.0	0.0	17.0	30.0	56.7	0.0	0.0		12.0	13.0	92.3	64.4	8.0	10.0	3.0	39	18	3	1	0	3	3	+5
24	Shaquille O'Neal S. O'Neal	1	45	35.1	45.0	11.0	2.0	3.0	1.0	20.0	25.0	80.0	0.0	0.0		5.0	8.0	62.5	78.9	3.0	8.0	3.0	35	11	2	3	1	3	4	+17
25	Gary Payton G. Payton	1	40	46.0	40.0	3.0	10.0	2.0	0.0	19.0	30.0	63.3	1.0	2.0	50.0	1.0	2.0	50.0	64.8	0.0	3.0	1.0	46	3	10	2	0	1	3	+2