A member of a pair (n, m) such that there exist another number σ(n) - n = m and σ(m) - m = n. more
The first 600 amicable numbers :
220,
284,
1184,
1210,
2620,
2924,
5020,
5564,
6232,
6368,
10744,
10856,
12285,
14595,
17296,
18416,
63020,
66928,
66992,
67095,
69615,
71145,
76084,
79750,
87633,
88730,
100485,
122265,
122368,
123152,
124155,
139815,
141664,
142310,
153176,
168730,
171856,
176272,
176336,
180848,
185368,
196724,
202444,
203432,
280540,
308620,
319550,
356408,
365084,
389924,
399592,
430402,
437456,
455344,
469028,
486178,
503056,
514736,
522405,
525915,
600392,
609928,
624184,
635624,
643336,
652664,
667964,
669688,
686072,
691256,
712216,
726104,
783556,
796696,
802725,
863835,
879712,
898216,
901424,
947835,
980984,
998104,
1043096,
1077890,
1099390,
1125765,
1154450,
1156870,
1175265,
1185376,
1189150,
1280565,
1286744,
1292570,
1328470,
1340235,
1358595,
1392368,
1438983,
1464592,
1466150,
1468324,
1483850,
1486845,
1511930,
1598470,
1669910,
1747930,
1749212,
1798875,
1870245,
2062570,
2082464,
2090656,
2236570,
2429030,
2652728,
2723792,
2728726,
2739704,
2802416,
2803580,
2874064,
2928136,
2941672,
2947216,
3077354,
3276856,
3606850,
3716164,
3721544,
3786904,
3805264,
3892670,
4006736,
4238984,
4246130,
4259750,
4300136,
4314616,
4445050,
4482765,
4488910,
4532710,
4604776,
5120595,
5123090,
5147032,
5162744,
5232010,
5357625,
5385310,
5459176,
5495264,
5504110,
5684679,
5726072,
5730615,
5799542,
5812130,
5843048,
5864660,
6088905,
6135962,
6329416,
6369928,
6371384,
6377175,
6680025,
6955216,
6993610,
7158710,
7275532,
7288930,
7418864,
7471508,
7489112,
7489324,
7577350,
7674088,
7677248,
7684672,
7800544,
7850512,
7916696,
8052488,
8221598,
8262136,
8369864,
8493050,
8619765,
8666860,
8754130,
8826070,
9071685,
9199496,
9206925,
9339704,
9363584,
9437056,
9478910,
9491625,
9498555,
9592504,
9627915,
9660950,
9773505,
9892936,
10025290,
10043690,
10254970,
10273670,
10533296,
10572550,
10596368,
10634085,
10638356,
10791795,
10854650,
10893230,
10949704,
10950615,
10992735,
11049730,
11173460,
11199112,
11252648,
11498355,
11545616,
11693290,
11791935,
11905504,
12024045,
12070305,
12101272,
12247504,
12361622,
12397552,
12707704,
13136528,
13212076,
13337336,
13671735,
13813150,
13921528,
13985672,
14084763,
14236136,
14310050,
14311688,
14426230,
14443730,
14654150,
14718712,
15002464,
15334304,
15363832,
15877065,
15882670,
15938055,
16137628,
16150628,
16517768,
16817050,
16871582,
17041010,
17257695,
17308665,
17578785,
17754165,
17844255,
17908064,
18017056,
18056312,
18087818,
18166888,
18194715,
18655744,
19150222,
19154336,
19325698,
19895265,
19985355,
20014808,
20022328,
20308995,
20955645,
21448630,
21457192,
22227075,
22240485,
22249552,
22508145,
22608632,
22823432,
23030090,
23111055,
23358248,
23389695,
23628940,
24472180,
24644925,
25132545,
25233112,
25325528,
25596544,
25640096,
25775368,
25966832,
26090325,
26138475,
26529808,
27428276,
28118032,
28128368,
28608424,
29603576,
30395276,
30724694,
30830696,
31536855,
31652704,
31818952,
32148585,
32174506,
32205616,
32642324,
32685250,
33501825,
34256222,
34352624,
34364912,
34380688,
34538270,
34765731,
34860248,
35095276,
35115795,
35361326,
35373195,
35390008,
35472592,
35997346,
36136575,
36415664,
36939357,
37363095,
37784810,
37848915,
38400512,
38637016,
38663950,
38783992,
38807968,
38938288,
39202605,
39259592,
39944086,
40105845,
40117714,
40678184,
40912232,
41654408,
43096904,
43266285,
43362050,
44139856,
44916944,
45263384,
45663849,
46137016,
46237730,
46271745,
46521405,
46555250,
46715896,
46991890,
48471470,
48639032,
48641584,
48852176,
49125375,
49215166,
50997596,
51737764,
52695376,
52967368,
53011395,
55349570,
55880590,
56055872,
56208368,
56512610,
56598208,
56924192,
58580540,
59497888,
61319902,
61953512,
63560025,
63717615,
64562488,
65003175,
66011985,
66595130,
66854710,
67729064,
67738268,
68891992,
69439576,
70507972,
71015260,
71241830,
71946890,
72958556,
73032872,
74055952,
74386305,
74733604,
74769345,
74824390,
75171808,
75226888,
75866014,
77237792,
78057370,
78088504,
78166448,
78437288,
78447010,
78469528,
79324875,
79732132,
80422335,
80960990,
81265112,
82633005,
82824255,
82977345,
83135650,
84521745,
84591405,
85458596,
85603550,
86158220,
87133365,
87354495,
87998470,
88110536,
88144630,
89477984,
89590995,
90437150,
91996816,
92143456,
93259184,
93837808,
94372450,
95629904,
95791430,
96304845,
96747315,
97041735,
97580944,
97945785,
99188788,
99899792,
102023145,
102358010,
102719740,
102814490,
103034776,
104177619,
104887448,
105016424,
105064552,
107908335,
108734050,
109410345,
110132055,
110960710,
114944072,
115187002,
115259625,
115447424,
115749344,
116251550,
116654896,
116970399,
116983744,
118458830,
118458976,
120115664,
120812175,
121293315,
123757335,
125222330,
125269528,
126671985,
127924335,
129063812,
131118975,
131483835,
131819506,
132692805,
132926625,
133089500,
133178325,
133471275,
133768816,
134312152,
134886465,
136549413,
136770075,
137424188,
138605350,
138690045,
139009990,
139057448,
140207067,
140744835,
140815384,
141213584,
141993412,
144788020,
145040288,
146648612,
147313850,
147366765,
147382335,
148077644,
148532625,
149364256,
153015550,
154190750,
155578180,
155709416,
155711205,
155797390,
156226856,
156322490,
157151410,
159017308,
160128436,
161088158,
162936904,
163634510,
164733752,
165181144,
165195890,
165323696,
165742395,
166212808,
166562685,
166679096,
166706530,
166737550,
167155024,
168392450,
168930032,
169000448,
169335790,
169652512,
169884784,
170566690,
172271385,
172610492,
173269088,
173499952,
173843216,
175032884,
175826716,
176374564,
176632390,
177997352,
179029010,
179904784,
180038452,
181088985,
182028483,
182108128,
182618810,
182622405,
182702024,
183408615,
184694055,
184713976,
186088988,
186753688,
186878110,
188953970,
189406984,
190055385,
190888155,
190889986,
193486028,
194594085,
195857415,
196214265,
196323170.
Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 77977 values, from 220 to 99999610625475).
n\r | 0 | 1 |
2 | 47586 | 30391 | 2 |
3 | 30391 | 23808 | 23778 | 3 |
4 | 30996 | 15189 | 16590 | 15202 | 4 |
5 | 38642 | 9785 | 9832 | 9868 | 9850 | 5 |
6 | 0 | 0 | 23778 | 30391 | 23808 | 0 | 6 |
7 | 18827 | 9640 | 9866 | 10147 | 10025 | 9809 | 9663 | 7 |
8 | 23399 | 7552 | 8306 | 7642 | 7597 | 7637 | 8284 | 7560 | 8 |
9 | 23980 | 8013 | 7824 | 3099 | 7936 | 7937 | 3312 | 7859 | 8017 | 9 |
10 | 13175 | 1251 | 8620 | 1130 | 8519 | 25467 | 8534 | 1212 | 8738 | 1331 | 10 |
11 | 20144 | 5780 | 5647 | 5845 | 5720 | 5818 | 5887 | 5881 | 5797 | 5634 | 5824 |
A pictorial representation of the table above
Imagine to divide the members of this family by a number n and compute the remainders. Should they be uniformly distributed, each remainder from 0 to n-1 would be obtained in about (1/n)-th of the cases. This outcome is represented by a white square. Reddish (resp. bluish) squares represent remainders which appear more (resp. less) frequently than 1/n.