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جدول مقسوم علیه ها
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توضیح
این جدول مقسوم علیه های برای اعداد 1 تا 1000 را در بر دارد.
توجه: تابع ضرب پذیر ( d( n:تعداد مقسوم علیههای مثبت n، شامل 1 و خود n؛ (σ( n: حاصل جمع تمام مقسوم علیههای مثبت n، شامل 1 و خود n. اعدادی که ناتام هستند
(σ( n)- n > n) با n+ نشان داده شده اند؛ و سه عددی که در جدول تام هستند (σ( n)- n = n) بصورت مورب ضخیم نشان داده شدهاند.
جدول
| n
| مقسوم علیه
| d(n)
| σ(n)
| σ(n)-n
| n
| مقسوم علیه
| d(n)
| σ(n)
| σ(n)-n
|
| 1
| 1
| 1
| 1
| 0-
| 501
| 1,3,167,501
| 4
| 672
| 171-
|
| 2
| 1,2
| 2
| 3
| 1-
| 502
| 1,2,251,502
| 4
| 756
| 254-
|
| 3
| 1,3
| 2
| 4
| 1-
| 503
| 1,503
| 2
| 504
| 1-
|
| 4
| 1,2,4
| 3
| 7
| 3-
| 504
| 1,2,3,4,6,
7,8,9,12,14,
18,21,24,28,36,
42,56,63,72,84,
126,168,252,504
| 24
| 1560
| 1056+
|
| 5
| 1,5
| 2
| 6
| 1-
| 505
| 1,5,101,505
| 4
| 612
| 107-
|
| 6
| 1,2,3,6
| 4
| 12
| 6
| 506
| 1,2,11,22,23,
46,253,506
| 8
| 864
| 358-
|
| 7
| 1,7
| 2
| 8
| 1-
| 507
| 1,3,13,39,169,
507
| 6
| 732
| 225-
|
| 8
| 1,2,4,8
| 4
| 15
| 7-
| 508
| 1,2,4,127,254,
508
| 6
| 896
| 388-
|
| 9
| 1,3,9
| 3
| 13
| 4-
| 509
| 1,509
| 2
| 510
| 1-
|
| 10
| 1,2,5,10
| 4
| 18
| 8-
| 510
| 1,2,3,5,6,
10,15,17,30,34,
51,85,102,170,255,
510
| 16
| 1296
| 786+
|
| 11
| 1,11
| 2
| 12
| 1-
| 511
| 1,7,73,511
| 4
| 592
| 81-
|
| 12
| 1,2,3,4,6,
12
| 6
| 28
| 16+
| 512
| 1,2,4,8,16,
32,64,128,256,512
| 10
| 1023
| 511-
|
| 13
| 1,13
| 2
| 14
| 1-
| 513
| 1,3,9,19,27,
57,171,513
| 8
| 800
| 287-
|
| 14
| 1,2,7,14
| 4
| 24
| 10-
| 514
| 1,2,257,514
| 4
| 774
| 260-
|
| 15
| 1,3,5,15
| 4
| 24
| 9-
| 515
| 1,5,103,515
| 4
| 624
| 109-
|
| 16
| 1,2,4,8,16
| 5
| 31
| 15-
| 516
| 1,2,3,4,6,
12,43,86,129,172,
258,516
| 12
| 1232
| 716+
|
| 17
| 1,17
| 2
| 18
| 1-
| 517
| 1,11,47,517
| 4
| 576
| 59-
|
| 18
| 1,2,3,6,9,
18
| 6
| 39
| 21+
| 518
| 1,2,7,14,37,
74,259,518
| 8
| 912
| 394-
|
| 19
| 1,19
| 2
| 20
| 1-
| 519
| 1,3,173,519
| 4
| 696
| 177-
|
| 20
| 1,2,4,5,10,
20
| 6
| 42
| 22+
| 520
| 1,2,4,5,8,
10,13,20,26,40,
52,65,104,130,260,
520
| 16
| 1260
| 740+
|
| 21
| 1,3,7,21
| 4
| 32
| 11-
| 521
| 1,521
| 2
| 522
| 1-
|
| 22
| 1,2,11,22
| 4
| 36
| 14-
| 522
| 1,2,3,6,9,
18,29,58,87,174,
261,522
| 12
| 1170
| 648+
|
| 23
| 1,23
| 2
| 24
| 1-
| 523
| 1,523
| 2
| 524
| 1-
|
| 24
| 1,2,3,4,6,
8,12,24
| 8
| 60
| 36+
| 524
| 1,2,4,131,262,
524
| 6
| 924
| 400-
|
| 25
| 1,5,25
| 3
| 31
| 6-
| 525
| 1,3,5,7,15,
21,25,35,75,105,
175,525
| 12
| 992
| 467-
|
| 26
| 1,2,13,26
| 4
| 42
| 16-
| 526
| 1,2,263,526
| 4
| 792
| 266-
|
| 27
| 1,3,9,27
| 4
| 40
| 13-
| 527
| 1,17,31,527
| 4
| 576
| 49-
|
| 28
| 1,2,4,7,14,
28
| 6
| 56
| 28
| 528
| 1,2,3,4,6,
8,11,12,16,22,
24,33,44,48,66,
88,132,176,264,528
| 20
| 1488
| 960+
|
| 29
| 1,29
| 2
| 30
| 1-
| 529
| 1,23,529
| 3
| 553
| 24-
|
| 30
| 1,2,3,5,6,
10,15,30
| 8
| 72
| 42+
| 530
| 1,2,5,10,53,
106,265,530
| 8
| 972
| 442-
|
| 31
| 1,31
| 2
| 32
| 1-
| 531
| 1,3,9,59,177,
531
| 6
| 780
| 249-
|
| 32
| 1,2,4,8,16,
32
| 6
| 63
| 31-
| 532
| 1,2,4,7,14,
19,28,38,76,133,
266,532
| 12
| 1120
| 588+
|
| 33
| 1,3,11,33
| 4
| 48
| 15-
| 533
| 1,13,41,533
| 4
| 588
| 55-
|
| 34
| 1,2,17,34
| 4
| 54
| 20-
| 534
| 1,2,3,6,89,
178,267,534
| 8
| 1080
| 546+
|
| 35
| 1,5,7,35
| 4
| 48
| 13-
| 535
| 1,5,107,535
| 4
| 648
| 113-
|
| 36
| 1,2,3,4,6,
9,12,18,36
| 9
| 91
| 55+
| 536
| 1,2,4,8,67,
134,268,536
| 8
| 1020
| 484-
|
| 37
| 1,37
| 2
| 38
| 1-
| 537
| 1,3,179,537
| 4
| 720
| 183-
|
| 38
| 1,2,19,38
| 4
| 60
| 22-
| 538
| 1,2,269,538
| 4
| 810
| 272-
|
| 39
| 1,3,13,39
| 4
| 56
| 17-
| 539
| 1,7,11,49,77,
539
| 6
| 684
| 145-
|
| 40
| 1,2,4,5,8,
10,20,40
| 8
| 90
| 50+
| 540
| 1,2,3,4,5,
6,9,10,12,15,
18,20,27,30,36,
45,54,60,90,108,
135,180,270,540
| 24
| 1680
| 1140+
|
| 41
| 1,41
| 2
| 42
| 1-
| 541
| 1,541
| 2
| 542
| 1-
|
| 42
| 1,2,3,6,7,
14,21,42
| 8
| 96
| 54+
| 542
| 1,2,271,542
| 4
| 816
| 274-
|
| 43
| 1,43
| 2
| 44
| 1-
| 543
| 1,3,181,543
| 4
| 728
| 185-
|
| 44
| 1,2,4,11,22,
44
| 6
| 84
| 40-
| 544
| 1,2,4,8,16,
17,32,34,68,136,
272,544
| 12
| 1134
| 590+
|
| 45
| 1,3,5,9,15,
45
| 6
| 78
| 33-
| 545
| 1,5,109,545
| 4
| 660
| 115-
|
| 46
| 1,2,23,46
| 4
| 72
| 26-
| 546
| 1,2,3,6,7,
13,14,21,26,39,
42,78,91,182,273,
546
| 16
| 1344
| 798+
|
| 47
| 1,47
| 2
| 48
| 1-
| 547
| 1,547
| 2
| 548
| 1-
|
| 48
| 1,2,3,4,6,
8,12,16,24,48
| 10
| 124
| 76+
| 548
| 1,2,4,137,274,
548
| 6
| 966
| 418-
|
| 49
| 1,7,49
| 3
| 57
| 8-
| 549
| 1,3,9,61,183,
549
| 6
| 806
| 257-
|
| 50
| 1,2,5,10,25,
50
| 6
| 93
| 43-
| 550
| 1,2,5,10,11,
22,25,50,55,110,
275,550
| 12
| 1116
| 566+
|
| 51
| 1,3,17,51
| 4
| 72
| 21-
| 551
| 1,19,29,551
| 4
| 600
| 49-
|
| 52
| 1,2,4,13,26,
52
| 6
| 98
| 46-
| 552
| 1,2,3,4,6,
8,12,23,24,46,
69,92,138,184,276,
552
| 16
| 1440
| 888+
|
| 53
| 1,53
| 2
| 54
| 1-
| 553
| 1,7,79,553
| 4
| 640
| 87-
|
| 54
| 1,2,3,6,9,
18,27,54
| 8
| 120
| 66+
| 554
| 1,2,277,554
| 4
| 834
| 280-
|
| 55
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