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تاریخچه ی: جدول مقسوم علیه ها
نگارش: 2
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
| 1,5,11,55
| 4
| 72
| 17-
| 555
| 1,3,5,15,37,
111,185,555
| 8
| 912
| 357-
|
56
| 1,2,4,7,8,
14,28,56
| 8
| 120
| 64+
| 556
| 1,2,4,139,278,
556
| 6
| 980
| 424-
|
57
| 1,3,19,57
| 4
| 80
| 23-
| 557
| 1,557
| 2
| 558
| 1-
|
58
| 1,2,29,58
| 4
| 90
| 32-
| 558
| 1,2,3,6,9,
18,31,62,93,186,
279,558
| 12
| 1248
| 690+
|
59
| 1,59
| 2
| 60
| 1-
| 559
| 1,13,43,559
| 4
| 616
| 57-
|
60
| 1,2,3,4,5,
6,10,12,15,20,
30,60
| 12
| 168
| 108+
| 560
| 1,2,4,5,7,
8,10,14,16,20,
28,35,40,56,70,
80,112,140,280,560
| 20
| 1488
| 928+
|
61
| 1,61
| 2
| 62
| 1-
| 561
| 1,3,11,17,33,
51,187,561
| 8
| 864
| 303-
|
62
| 1,2,31,62
| 4
| 96
| 34-
| 562
| 1,2,281,562
| 4
| 846
| 284-
|
63
| 1,3,7,9,21,
63
| 6
| 104
| 41-
| 563
| 1,563
| 2
| 564
| 1-
|
64
| 1,2,4,8,16,
32,64
| 7
| 127
| 63-
| 564
| 1,2,3,4,6,
12,47,94,141,188,
282,564
| 12
| 1344
| 780+
|
65
| 1,5,13,65
| 4
| 84
| 19-
| 565
| 1,5,113,565
| 4
| 684
| 119-
|
66
| 1,2,3,6,11,
22,33,66
| 8
| 144
| 78+
| 566
| 1,2,283,566
| 4
| 852
| 286-
|
67
| 1,67
| 2
| 68
| 1-
| 567
| 1,3,7,9,21,
27,63,81,189,567
| 10
| 968
| 401-
|
68
| 1,2,4,17,34,
68
| 6
| 126
| 58-
| 568
| 1,2,4,8,71,
142,284,568
| 8
| 1080
| 512-
|
69
| 1,3,23,69
| 4
| 96
| 27-
| 569
| 1,569
| 2
| 570
| 1-
|
70
| 1,2,5,7,10,
14,35,70
| 8
| 144
| 74+
| 570
| 1,2,3,5,6,
10,15,19,30,38,
57,95,114,190,285,
570
| 16
| 1440
| 870+
|
71
| 1,71
| 2
| 72
| 1-
| 571
| 1,571
| 2
| 572
| 1-
|
72
| 1,2,3,4,6,
8,9,12,18,24,
36,72
| 12
| 195
| 123+
| 572
| 1,2,4,11,13,
22,26,44,52,143,
286,572
| 12
| 1176
| 604+
|
73
| 1,73
| 2
| 74
| 1-
| 573
| 1,3,191,573
| 4
| 768
| 195-
|
74
| 1,2,37,74
| 4
| 114
| 40-
| 574
| 1,2,7,14,41,
82,287,574
| 8
| 1008
| 434-
|
75
| 1,3,5,15,25,
75
| 6
| 124
| 49-
| 575
| 1,5,23,25,115,
575
| 6
| 744
| 169-
|
76
| 1,2,4,19,38,
76
| 6
| 140
| 64-
| 576
| 1,2,3,4,6,
8,9,12,16,18,
24,32,36,48,64,
72,96,144,192,288,
576
| 21
| 1651
| 1075+
|
77
| 1,7,11,77
| 4
| 96
| 19-
| 577
| 1,577
| 2
| 578
| 1-
|
78
| 1,2,3,6,13,
26,39,78
| 8
| 168
| 90+
| 578
| 1,2,17,34,289,
578
| 6
| 921
| 343-
|
79
| 1,79
| 2
| 80
| 1-
| 579
| 1,3,193,579
| 4
| 776
| 197-
|
80
| 1,2,4,5,8,
10,16,20,40,80
| 10
| 186
| 106+
| 580
| 1,2,4,5,10,
20,29,58,116,145,
290,580
| 12
| 1260
| 680+
|
81
| 1,3,9,27,81
| 5
| 121
| 40-
| 581
| 1,7,83,581
| 4
| 672
| 91-
|
82
| 1,2,41,82
| 4
| 126
| 44-
| 582
| 1,2,3,6,97,
194,291,582
| 8
| 1176
| 594+
|
83
| 1,83
| 2
| 84
| 1-
| 583
| 1,11,53,583
| 4
| 648
| 65-
|
84
| 1,2,3,4,6,
7,12,14,21,28,
42,84
| 12
| 224
| 140+
| 584
| 1,2,4,8,73,
146,292,584
| 8
| 1110
| 526-
|
85
| 1,5,17,85
| 4
| 108
| 23-
| 585
| 1,3,5,9,13,
15,39,45,65,117,
195,585
| 12
| 1092
| 507-
|
86
| 1,2,43,86
| 4
| 132
| 46-
| 586
| 1,2,293,586
| 4
| 882
| 296-
|
87
| 1,3,29,87
| 4
| 120
| 33-
| 587
| 1,587
| 2
| 588
| 1-
|
88
| 1,2,4,8,11,
22,44,88
| 8
| 180
| 92+
| 588
| 1,2,3,4,6,
7,12,14,21,28,
42,49,84,98,147,
196,294,588
| 18
| 1596
| 1008+
|
89
| 1,89
| 2
| 90
| 1-
| 589
| 1,19,31,589
| 4
| 640
| 51-
|
90
| 1,2,3,5,6,
9,10,15,18,30,
45,90
| 12
| 234
| 144+
| 590
| 1,2,5,10,59,
118,295,590
| 8
| 1080
| 490-
|
91
| 1,7,13,91
| 4
| 112
| 21-
| 591
| 1,3,197,591
| 4
| 792
| 201-
|
92
| 1,2,4,23,46,
92
| 6
| 168
| 76-
| 592
| 1,2,4,8,16,
37,74,148,296,592
| 10
| 1178
| 586-
|
93
| 1,3,31,93
| 4
| 128
| 35-
| 593
| 1,593
| 2
| 594
| 1-
|
94
| 1,2,47,94
| 4
| 144
| 50-
| 594
| 1,2,3,6,9,
11,18,22,27,33,
54,66,99,198,297,
594
| 16
| 1440
| 846+
|
95
| 1,5,19,95
| 4
| 120
| 25-
| 595
| 1,5,7,17,35,
85,119,595
| 8
| 864
| 269-
|
96
| 1,2,3,4,6,
8,12,16,24,32,
48,96
| 12
| 252
| 156+
| 596
| 1,2,4,149,298,
596
| 6
| 1050
| 454-
|
97
| 1,97
| 2
| 98
| 1-
| 597
| 1,3,199,597
| 4
| 800
| 203-
|
98
| 1,2,7,14,49,
98
| 6
| 171
| 73-
| 598
| 1,2,13,23,26,
46,299,598
| 8
| 1008
| 410-
|
99
| 1,3,9,11,33,
99
| 6
| 156
| 57-
| 599
| 1,599
| 2
| 600
| 1-
|
100
| 1,2,4,5,10,
20,25,50,100
| 9
| 217
| 117+
| 600
| 1,2,3,4,5,
6,8,10,12,15,
20,24,25,30,40,
50,60,75,100,120,
150,200,300,600
| 24
| 1860
| 1260+
|
101
| 1,101
| 2
| 102
| 1-
| 601
| 1,601
| 2
| 602
| 1-
|
102
| 1,2,3,6,17,
34,51,102
| 8
| 216
| 114+
| 602
| 1,2,7,14,43,
86,301,602
| 8
| 1056
| 454-
|
103
| 1,103
| 2
| 104
| 1-
| 603
| 1,3,9,67,201,
603
| 6
| 884
| 281-
|
104
| 1,2,4,8,13,
26,52,104
| 8
| 210
| 106+
| 604
| 1,2,4,151,302,
604
| 6
| 1064
| 460-
|
105
| 1,3,5,7,15,
21,35,105
| 8
| 192
| 87-
| 605
| 1,5,11,55,121,
605
| 6
| 798
| 193-
|
106
| 1,2,53,106
| 4
| 162
| 56-
| 606
| 1,2,3,6,101,
202,303,606
| 8
| 1224
| 618+
|
107
| 1,107
| 2
| 108
| 1-
| 607
| 1,607
| 2
| 608
| 1-
|
108
| 1,2,3,4,6,
9,12,18,27,36,
54,108
| 12
| 280
| 172+
| 608
| 1,2,4,8,16,
19,32,38,76,152,
304,608
| 12
| 1260
| 652+
|
109
| 1,109
| 2
| 110
| 1-
| 609
| 1,3,7,21,29,
87,203,609
| 8
| 960
| 351-
|
110
| 1,2,5,10,11,
22,55,110
| 8
| 216
| 106-
| 610
| 1,2,5,10,61,
122,305,610
| 8
| 1116
| 506-
|
111
| 1,3,37,111
| 4
| 152
| 41-
| 611
| 1,13,47,611
| 4
| 672
| 61-
|
112
| 1,2,4,7,8,
14,16,28,56,112
| 10
| 248
| 136+
| 612
| 1,2,3,4,6,
9,12,17,18,34,
36,51,68,102,153,
204,306,612
| 18
| 1638
| 1026+
|
113
| 1,113
| 2
| 114
| 1-
| 613
| 1,613
| 2
| 614
| 1-
|
114
| 1,2,3,6,19,
38,57,114
| 8
| 240
| 126+
| 614
| 1,2,307,614
| 4
| 924
| 310-
|
115
| 1,5,23,115
| 4
| 144
| 29-
| 615
| 1,3,5,15,41,
123,205,615
| 8
| 1008
| 393-
|
116
| 1,2,4,29,58,
116
| 6
| 210
| 94-
| 616
| 1,2,4,7,8,
11,14,22,28,44,
56,77,88,154,308,
616
| 16
| 1440
| 824+
|
117
| 1,3,9,13,39,
117
| 6
| 182
| 65-
| 617
| 1,617
| 2
| 618
| 1-
|
118
| 1,2,59,118
| 4
| 180
| 62-
| 618
| 1,2,3,6,103,
206,309,618
| 8
| 1248
| 630+
|
119
| 1,7,17,119
| 4
| 144
| 25-
| 619
| 1,619
| 2
| 620
| 1-
|
120
| 1,2,3,4,5,
6,8,10,12,15,
20,24,30,40,60,
120
| 16
| 360
| 240+
| 620
| 1,2,4,5,10,
20,31,62,124,155,
310,620
| 12
| 1344
| 724+
|
121
| 1,11,121
| 3
| 133
| 12-
| 621
| 1,3,9,23,27,
69,207,621
| 8
| 960
| 339-
|
122
| 1,2,61,122
| 4
| 186
| 64-
| 622
| 1,2,311,622
| 4
| 936
| 314-
|
123
| 1,3,41,123
| 4
| 168
| 45-
| 623
| 1,7,89,623
| 4
| 720
| 97-
|
124
| 1,2,4,31,62,
124
| 6
| 224
| 100-
| 624
| 1,2,3,4,6,
8,12,13,16,24,
26,39,48,52,78,
104,156,208,312,624
| 20
| 1736
| 1112+
|
125
| 1,5,25,125
| 4
| 156
| 31-
| 625
| 1,5,25,125,625
| 5
| 781
| 156-
|
126
| 1,2,3,6,7,
9,14,18,21,42,
63,126
| 12
| 312
| 186+
| 626
| 1,2,313,626
| 4
| 942
| 316-
|
127
| 1,127
| 2
| 128
| 1-
| 627
| 1,3,11,19,33,
57,209,627
| 8
| 960
| 333-
|
128
| 1,2,4,8,16,
32,64,128
| 8
| 255
| 127-
| 628
| 1,2,4,157,314,
628
| 6
| 1106
| 478-
|
129
| 1,3,43,129
| 4
| 176
| 47-
| 629
| 1,17,37,629
| 4
| 684
| 55-
|
130
| 1,2,5,10,13,
26,65,130
| 8
| 252
| 122-
| 630
| 1,2,3,5,6,
7,9,10,14,15,
18,21,30,35,42,
45,63,70,90,105,
126,210,315,630
| 24
| 1872
| 1242+
|
((
|
|
|