A number which is abundant but not pseudoperfect. more
The first 600 weird numbers :
70,
836,
4030,
5830,
7192,
7912,
9272,
10430,
10570,
10792,
10990,
11410,
11690,
12110,
12530,
12670,
13370,
13510,
13790,
13930,
14770,
15610,
15890,
16030,
16310,
16730,
16870,
17272,
17570,
17990,
18410,
18830,
18970,
19390,
19670,
19810,
20510,
21490,
21770,
21910,
22190,
23170,
23590,
24290,
24430,
24710,
25130,
25690,
26110,
26530,
26810,
27230,
27790,
28070,
28630,
29330,
29470,
30170,
30310,
30730,
31010,
31430,
31990,
32270,
32410,
32690,
33530,
34090,
34370,
34930,
35210,
35630,
36470,
36610,
37870,
38290,
38990,
39410,
39830,
39970,
40390,
41090,
41510,
41930,
42070,
42490,
42910,
43190,
43330,
44170,
44870,
45010,
45290,
45356,
45710,
46130,
46270,
47110,
47390,
47810,
48370,
49070,
49630,
50330,
50890,
51310,
51730,
52010,
52570,
52990,
53270,
53830,
54110,
55090,
55790,
56630,
56770,
57470,
57610,
57890,
58030,
58730,
59710,
59990,
60130,
60410,
61390,
61670,
61810,
62090,
63490,
63770,
64330,
65030,
65590,
65870,
66290,
66710,
67690,
67970,
68390,
68810,
69370,
69790,
70630,
70910,
71330,
71470,
72170,
72310,
72730,
73430,
73570,
73616,
74270,
74410,
74830,
76090,
76370,
76510,
76790,
77210,
77630,
78190,
78610,
79030,
80570,
80710,
81410,
81970,
82670,
83090,
83312,
83510,
84070,
84910,
85190,
85610,
86030,
86170,
86590,
87430,
88130,
89390,
89530,
89810,
90230,
90370,
90790,
91070,
91210,
91388,
91490,
92330,
92470,
92890,
95270,
95690,
96110,
96670,
97930,
98630,
99610,
99890,
100030,
100310,
100730,
101290,
101570,
101710,
102130,
102970,
103670,
103810,
104090,
104230,
104510,
104930,
105770,
106610,
107170,
108010,
108430,
108710,
109130,
109690,
109970,
110530,
110810,
111790,
112070,
112490,
112630,
112910,
113072,
113330,
113470,
113890,
114590,
115990,
116410,
116690,
116830,
118510,
118790,
118930,
119630,
120470,
120610,
121310,
121870,
122290,
122710,
123130,
124390,
124810,
125090,
125230,
126070,
126770,
127610,
128170,
129290,
130270,
130690,
130970,
131110,
131390,
131530,
132230,
133070,
133490,
133910,
135170,
135310,
136430,
136570,
138110,
138530,
139090,
139510,
139790,
139930,
140210,
140770,
141190,
141890,
142030,
142730,
143710,
144410,
144830,
145670,
145810,
146090,
146230,
146930,
147770,
147910,
149030,
149170,
149590,
149870,
150010,
150710,
151270,
152530,
154210,
154490,
154910,
155470,
156590,
156730,
157010,
157570,
158690,
158830,
159110,
159670,
160090,
160510,
160790,
161630,
161770,
163310,
163730,
163870,
164290,
164570,
164990,
165970,
166390,
166670,
166810,
167230,
167510,
167930,
168770,
169190,
169610,
170590,
170870,
171290,
172130,
172690,
173110,
173390,
175210,
176470,
177170,
177730,
178010,
178430,
178570,
178990,
180530,
181370,
181510,
182630,
183190,
183470,
184310,
185290,
185990,
186130,
186410,
186970,
187390,
187810,
188090,
188230,
188510,
188930,
189490,
189770,
189910,
190330,
191030,
191170,
191870,
192430,
192710,
193690,
194390,
195230,
195370,
195790,
196070,
196210,
197330,
198310,
198590,
199010,
199570,
199990,
200270,
201530,
202090,
202790,
203210,
203630,
204190,
204890,
205730,
206710,
206990,
207410,
207830,
207970,
209930,
210070,
210770,
211330,
211610,
212590,
212870,
213430,
214270,
214690,
215530,
215810,
216230,
217630,
218330,
218470,
219590,
221410,
221690,
221830,
222670,
222952,
223090,
223370,
224210,
224630,
225190,
225470,
226030,
227570,
227710,
227990,
228130,
228970,
230930,
231070,
231490,
231910,
232330,
232610,
233030,
233170,
234010,
234290,
235130,
235270,
235970,
236110,
237230,
237370,
238490,
238910,
240310,
241430,
241990,
242270,
242410,
242690,
242830,
243892,
244370,
244930,
245770,
246190,
246890,
247030,
247310,
247730,
247870,
248290,
248990,
249130,
249970,
250670,
250810,
251510,
252490,
252910,
253190,
253610,
254012,
254170,
254590,
255010,
256130,
256970,
257110,
257390,
258370,
258790,
259070,
259630,
260330,
260890,
261310,
261730,
263270,
263690,
263830,
264530,
265510,
265790,
266210,
267470,
267610,
268310,
269290,
269570,
269710,
270410,
271390,
271670,
272230,
273490,
273770,
274190,
274330,
274610,
275030,
275170,
276010,
276290,
277690,
279230,
280070,
280210,
280490,
280910,
281330,
281470,
281890,
283430,
283570,
283990,
285110,
285530,
286370,
286510,
286930,
287770,
288890,
289030,
289310,
289730,
290710,
290990,
291130,
292390,
294070,
294770,
295190,
295330,
296030,
296170,
296870,
297010,
297710,
298130,
298270,
298970,
299110,
299810,
300230,
300790,
302890,
303590,
303730,
304430,
304990,
305410,
306110,
307370,
307790,
308630,
309470,
309610,
310870,
311290,
311570,
311990,
312410,
313670,
313810,
314510,
315490,
315910,
316190,
316330,
316610,
318290,
318430.
Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 7784 values, from 70 to 4999330).
n\r | 0 | 1 |
2 | 7784 | 0 | 2 |
3 | 0 | 3891 | 3893 | 3 |
4 | 718 | 0 | 7066 | 0 | 4 |
5 | 7066 | 180 | 189 | 180 | 169 | 5 |
6 | 0 | 0 | 3893 | 0 | 3891 | 0 | 6 |
7 | 7063 | 119 | 124 | 125 | 118 | 121 | 114 | 7 |
8 | 27 | 0 | 3533 | 0 | 691 | 0 | 3533 | 0 | 8 |
9 | 0 | 1305 | 1298 | 0 | 1304 | 1300 | 0 | 1282 | 1295 | 9 |
10 | 7066 | 0 | 189 | 0 | 169 | 0 | 180 | 0 | 180 | 0 | 10 |
11 | 689 | 707 | 706 | 708 | 708 | 713 | 713 | 716 | 712 | 707 | 705 |
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.