A number of the form A⋅BA for A, B > 1. more
The first 600 ABA numbers :
8,
18,
24,
32,
50,
64,
72,
81,
98,
128,
160,
162,
192,
200,
242,
288,
324,
338,
375,
384,
392,
450,
512,
578,
648,
722,
800,
882,
896,
968,
1024,
1029,
1058,
1152,
1215,
1250,
1352,
1458,
1536,
1568,
1682,
1800,
1922,
2048,
2178,
2187,
2312,
2450,
2500,
2592,
2738,
2888,
3000,
3042,
3200,
3362,
3528,
3698,
3872,
3993,
4050,
4232,
4374,
4418,
4608,
4802,
5000,
5120,
5184,
5202,
5408,
5618,
5832,
6050,
6272,
6498,
6591,
6728,
6962,
7200,
7442,
7688,
7938,
8192,
8232,
8450,
8712,
8978,
9248,
9522,
9604,
9800,
10082,
10125,
10240,
10368,
10658,
10952,
11250,
11552,
11858,
12168,
12288,
12482,
12800,
13122,
13448,
13778,
14112,
14450,
14739,
14792,
15138,
15309,
15488,
15625,
15842,
16200,
16384,
16562,
16928,
17298,
17496,
17672,
18050,
18432,
18818,
19208,
19602,
20000,
20402,
20577,
20808,
21218,
21632,
22050,
22472,
22528,
22898,
23328,
23762,
24000,
24200,
24576,
24642,
25088,
25538,
25992,
26244,
26450,
26912,
27378,
27783,
27848,
28322,
28800,
29282,
29768,
30258,
30752,
31250,
31752,
31944,
32258,
32768,
33282,
33800,
34322,
34848,
35378,
35912,
36450,
36501,
36992,
37538,
38088,
38642,
38880,
39200,
39762,
40000,
40328,
40898,
41472,
42050,
42632,
43218,
43808,
44402,
45000,
45602,
46208,
46818,
46875,
47432,
48050,
48672,
49152,
49298,
49928,
50562,
51200,
51842,
52488,
52728,
53138,
53792,
54450,
55112,
55778,
56448,
57122,
57800,
58482,
58564,
59049,
59168,
59858,
60552,
61250,
61952,
62658,
63368,
64082,
64800,
65522,
65856,
66248,
66978,
67712,
68450,
69192,
69938,
70688,
71442,
72200,
72962,
73167,
73728,
74498,
75272,
76050,
76832,
77618,
78408,
79202,
80000,
80802,
81000,
81608,
82418,
82944,
83232,
84035,
84050,
84872,
85698,
86528,
87362,
88200,
89042,
89373,
89888,
90738,
91592,
92450,
93312,
93750,
94178,
95048,
95922,
96800,
97682,
98304,
98568,
99458,
100352,
101250,
102152,
103058,
103968,
104882,
105800,
106496,
106722,
107648,
107811,
108578,
109512,
110450,
111392,
112338,
113288,
114242,
114244,
114688,
115200,
116162,
117128,
117912,
118098,
119072,
120050,
121032,
122018,
123008,
124002,
125000,
126002,
127008,
128018,
128625,
129032,
130050,
131072,
132098,
133128,
134162,
135200,
136242,
137288,
138338,
139392,
139968,
140450,
141512,
142578,
143648,
144722,
145800,
146882,
147968,
149058,
150152,
151250,
151959,
152352,
153458,
153664,
154568,
155682,
156800,
157922,
159048,
160178,
161312,
162450,
163592,
163840,
164616,
164738,
165888,
167042,
168200,
169362,
170528,
171698,
172872,
174050,
175232,
176418,
177147,
177608,
177957,
178802,
180000,
181202,
182408,
183618,
184832,
186050,
187272,
188498,
189728,
190962,
192000,
192200,
193442,
194688,
195938,
197192,
198450,
199712,
200978,
202248,
202500,
203522,
204800,
206082,
206763,
207368,
208658,
209952,
211250,
212552,
213858,
215168,
216482,
217800,
219122,
220448,
221778,
222264,
223112,
224450,
225792,
227138,
228488,
229376,
229842,
231200,
232562,
233928,
235298,
236672,
238050,
238521,
239432,
240818,
242208,
243602,
245000,
246402,
247808,
249218,
250632,
252050,
253472,
254898,
255552,
256328,
257762,
259200,
260642,
262088,
262144,
263538,
264992,
266450,
267912,
269378,
270848,
272322,
273375,
273800,
275282,
276768,
278258,
279752,
279936,
281250,
282752,
284258,
285768,
287282,
288800,
290322,
291848,
292008,
293378,
294912,
295245,
296450,
297992,
299538,
301088,
302642,
304200,
305762,
307328,
308898,
310472,
311469,
312050,
313632,
315218,
316808,
318402,
320000,
321602,
323208,
324818,
326432,
328050,
329672,
331298,
331776,
332928,
334084,
334562,
336200,
337842,
339488,
341138,
342792,
344450,
346112,
347778,
349448,
351122,
352800,
352947,
354482,
356168,
357858,
359552,
361250,
362952,
364658,
366368,
368082,
369800,
371522,
373248,
374978,
375000,
376712,
378450,
380192,
381938,
383688,
385442,
387200,
388962,
390728,
392498,
394272,
396050,
397832,
397953,
399618,
401408,
403202,
405000,
406802,
408608,
410418,
412232,
414050,
415872,
417698,
419528,
419904,
421362,
421824,
423200,
425042,
426888,
428738,
430592,
432450,
434312,
436178,
438048,
439922,
441800,
443682,
445568,
446631,
447458,
449352,
451250,
453152,
455058,
456968,
458882,
460800,
462722,
464648,
466578,
468512,
470450,
472392,
474338,
476288,
478242,
480200,
482162,
484128,
486098,
488072,
490050,
491520,
492032,
494018,
496008,
498002,
499125,
500000,
502002,
504008,
506018,
508032,
510050,
512072,
514098,
516128,
518162,
520200,
521284.
Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 2252741 values, from 8 to 9999991256978).
n\r | 0 | 1 |
2 | 2245081 | 7660 | 2 |
3 | 760931 | 975 | 1490835 | 3 |
4 | 1126984 | 3829 | 1118097 | 3831 | 4 |
5 | 450786 | 3062 | 897417 | 897419 | 4057 | 5 |
6 | 753388 | 59 | 1490777 | 7543 | 916 | 58 | 6 |
7 | 321869 | 639285 | 639285 | 6451 | 645635 | 68 | 148 | 7 |
8 | 1126351 | 1914 | 1118040 | 1917 | 633 | 1915 | 57 | 1914 | 8 |
9 | 750891 | 326 | 496946 | 4988 | 326 | 496943 | 5052 | 323 | 496946 | 9 |
10 | 449139 | 1505 | 895916 | 1503 | 2553 | 1647 | 1557 | 1501 | 895916 | 1504 | 10 |
11 | 204801 | 1594 | 407934 | 1596 | 1601 | 1730 | 408058 | 407938 | 407937 | 1603 | 407949 |
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.