A number with distinct digits divisible by each of them. more
The full list of Lynch-Bell numbers is :
1,
2,
3,
4,
5,
6,
7,
8,
9,
12,
15,
24,
36,
48,
124,
126,
128,
132,
135,
162,
168,
175,
184,
216,
248,
264,
312,
315,
324,
384,
396,
412,
432,
612,
624,
648,
672,
728,
735,
784,
816,
824,
864,
936,
1236,
1248,
1296,
1326,
1362,
1368,
1395,
1632,
1692,
1764,
1824,
1926,
1935,
1962,
2136,
2184,
2196,
2316,
2364,
2436,
2916,
3126,
3162,
3168,
3195,
3216,
3264,
3276,
3492,
3612,
3624,
3648,
3816,
3864,
3915,
3924,
4128,
4172,
4236,
4368,
4392,
4632,
4872,
4896,
4932,
4968,
6132,
6192,
6312,
6324,
6384,
6432,
6912,
6984,
8136,
8496,
8736,
9126,
9135,
9162,
9216,
9315,
9324,
9432,
9612,
9648,
9864,
12384,
12648,
12768,
12864,
13248,
13824,
13896,
13968,
14328,
14728,
14832,
16248,
16824,
17248,
18264,
18432,
18624,
18936,
19368,
21384,
21648,
21784,
21864,
23184,
24168,
24816,
26184,
27384,
28416,
29736,
31248,
31824,
31896,
31968,
32184,
34128,
36792,
37128,
37296,
37926,
38472,
39168,
39816,
41328,
41832,
42168,
42816,
43128,
43176,
46128,
46872,
48216,
48312,
61248,
61824,
62184,
64128,
68712,
72184,
73164,
73248,
73416,
73962,
78624,
79128,
79632,
81264,
81432,
81624,
81936,
82416,
84216,
84312,
84672,
87192,
89136,
89712,
91368,
91476,
91728,
92736,
93168,
93816,
98136,
123648,
123864,
123984,
124368,
126384,
129384,
132648,
132864,
132984,
134928,
136248,
136824,
138264,
138624,
139248,
139824,
142368,
143928,
146328,
146832,
148392,
148632,
149328,
149832,
162384,
163248,
163824,
164328,
164832,
167328,
167832,
168432,
172368,
183264,
183624,
184392,
184632,
186432,
189432,
192384,
193248,
193824,
194328,
194832,
198432,
213648,
213864,
213984,
214368,
216384,
218736,
219384,
231648,
231864,
231984,
234168,
234816,
236184,
238416,
239184,
241368,
243168,
243768,
243816,
247968,
248136,
248976,
261384,
263184,
273168,
281736,
283416,
284136,
291384,
293184,
297864,
312648,
312864,
312984,
314928,
316248,
316824,
318264,
318624,
319248,
319824,
321648,
321864,
321984,
324168,
324816,
326184,
328416,
329184,
341928,
342168,
342816,
346128,
348192,
348216,
348912,
349128,
361248,
361824,
361872,
362184,
364128,
364728,
367248,
376824,
381264,
381624,
382416,
384192,
384216,
384912,
391248,
391824,
392184,
394128,
412368,
413928,
416328,
416832,
418392,
418632,
419328,
419832,
421368,
423168,
423816,
427896,
428136,
428736,
431928,
432168,
432768,
432816,
436128,
438192,
438216,
438912,
439128,
461328,
461832,
463128,
468312,
469728,
478296,
478632,
481392,
481632,
482136,
483192,
483216,
483672,
483912,
486312,
489312,
491328,
491832,
493128,
498312,
612384,
613248,
613824,
613872,
614328,
614832,
618432,
621384,
623184,
623784,
627984,
631248,
631824,
632184,
634128,
634872,
641328,
641832,
643128,
648312,
671328,
671832,
681432,
684312,
689472,
732648,
732816,
742896,
746928,
762384,
768432,
783216,
789264,
796824,
813264,
813624,
814392,
814632,
816432,
819432,
823416,
824136,
824376,
831264,
831624,
832416,
834192,
834216,
834912,
836472,
841392,
841632,
842136,
843192,
843216,
843912,
846312,
849312,
861432,
864312,
873264,
891432,
894312,
897624,
912384,
913248,
913824,
914328,
914832,
918432,
921384,
923184,
927864,
931248,
931824,
932184,
934128,
941328,
941832,
943128,
948312,
976248,
978264,
981432,
984312,
1289736,
1293768,
1369872,
1372896,
1376928,
1382976,
1679328,
1679832,
1687392,
1738296,
1823976,
1863792,
1876392,
1923768,
1936872,
1982736,
2137968,
2138976,
2189376,
2317896,
2789136,
2793168,
2819376,
2831976,
2931768,
2937816,
2978136,
2983176,
3186792,
3187296,
3196872,
3271968,
3297168,
3298176,
3619728,
3678192,
3712968,
3768912,
3796128,
3816792,
3817296,
3867192,
3869712,
3927168,
3928176,
6139728,
6379128,
6387192,
6389712,
6391728,
6719328,
6719832,
6731928,
6893712,
6913872,
6971328,
6971832,
7168392,
7198632,
7231896,
7291368,
7329168,
7361928,
7392168,
7398216,
7613928,
7639128,
7829136,
7836192,
7839216,
7861392,
7863912,
7891632,
7892136,
7916328,
7916832,
7921368,
8123976,
8163792,
8176392,
8219736,
8312976,
8367912,
8617392,
8731296,
8796312,
8912736,
8973216,
9163728,
9176328,
9176832,
9182376,
9231768,
9237816,
9278136,
9283176,
9617328,
9617832,
9678312,
9718632,
9723168,
9781632,
9782136,
9812376,
9867312.
Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 548 values, from 1 to 9867312).
n\r | 0 | 1 |
2 | 532 | 16 | 2 |
3 | 528 | 12 | 8 | 3 |
4 | 518 | 3 | 14 | 13 | 4 |
5 | 12 | 119 | 152 | 148 | 117 | 5 |
6 | 516 | 3 | 7 | 12 | 9 | 1 | 6 |
7 | 239 | 57 | 42 | 52 | 56 | 58 | 44 | 7 |
8 | 488 | 2 | 7 | 6 | 30 | 1 | 7 | 7 | 8 |
9 | 314 | 2 | 2 | 66 | 7 | 4 | 148 | 3 | 2 | 9 |
10 | 0 | 1 | 151 | 1 | 116 | 12 | 118 | 1 | 147 | 1 | 10 |
11 | 52 | 64 | 58 | 48 | 49 | 48 | 44 | 38 | 45 | 56 | 46 |
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.