A number divisible by each of its digits. more
The first 600 nude numbers :
1,
2,
3,
4,
5,
6,
7,
8,
9,
11,
12,
15,
22,
24,
33,
36,
44,
48,
55,
66,
77,
88,
99,
111,
112,
115,
122,
124,
126,
128,
132,
135,
144,
155,
162,
168,
175,
184,
212,
216,
222,
224,
244,
248,
264,
288,
312,
315,
324,
333,
336,
366,
384,
396,
412,
424,
432,
444,
448,
488,
515,
555,
612,
624,
636,
648,
666,
672,
728,
735,
777,
784,
816,
824,
848,
864,
888,
936,
999,
1111,
1112,
1113,
1115,
1116,
1122,
1124,
1128,
1131,
1144,
1155,
1164,
1176,
1184,
1197,
1212,
1222,
1224,
1236,
1244,
1248,
1266,
1288,
1296,
1311,
1326,
1332,
1335,
1344,
1362,
1368,
1395,
1412,
1416,
1424,
1444,
1448,
1464,
1488,
1515,
1555,
1575,
1626,
1632,
1644,
1662,
1692,
1715,
1722,
1764,
1771,
1824,
1848,
1888,
1926,
1935,
1944,
1962,
2112,
2122,
2124,
2128,
2136,
2144,
2166,
2184,
2196,
2212,
2222,
2224,
2226,
2232,
2244,
2248,
2262,
2288,
2316,
2322,
2328,
2364,
2412,
2424,
2436,
2444,
2448,
2488,
2616,
2622,
2664,
2688,
2744,
2772,
2824,
2832,
2848,
2888,
2916,
3111,
3126,
3132,
3135,
3144,
3162,
3168,
3171,
3195,
3216,
3222,
3264,
3276,
3288,
3312,
3315,
3324,
3333,
3336,
3339,
3366,
3384,
3393,
3432,
3444,
3492,
3555,
3612,
3624,
3636,
3648,
3666,
3717,
3816,
3864,
3888,
3915,
3924,
3933,
3996,
4112,
4116,
4124,
4128,
4144,
4164,
4172,
4184,
4212,
4224,
4236,
4244,
4248,
4288,
4332,
4344,
4368,
4392,
4412,
4416,
4424,
4444,
4448,
4464,
4488,
4632,
4644,
4824,
4848,
4872,
4888,
4896,
4932,
4968,
5115,
5155,
5355,
5515,
5535,
5555,
5775,
6126,
6132,
6144,
6162,
6168,
6192,
6216,
6222,
6264,
6288,
6312,
6324,
6336,
6366,
6384,
6432,
6444,
6612,
6624,
6636,
6648,
6666,
6696,
6762,
6816,
6864,
6888,
6912,
6966,
6984,
7112,
7119,
7175,
7224,
7266,
7371,
7448,
7476,
7644,
7728,
7777,
7784,
8112,
8128,
8136,
8144,
8184,
8224,
8232,
8248,
8288,
8328,
8424,
8448,
8488,
8496,
8616,
8664,
8688,
8736,
8824,
8832,
8848,
8888,
8928,
9126,
9135,
9144,
9162,
9216,
9288,
9315,
9324,
9333,
9396,
9432,
9612,
9648,
9666,
9864,
9936,
9999,
11111,
11112,
11115,
11122,
11124,
11128,
11133,
11136,
11144,
11155,
11166,
11172,
11184,
11196,
11212,
11222,
11224,
11226,
11232,
11244,
11248,
11262,
11288,
11313,
11316,
11322,
11328,
11331,
11355,
11364,
11412,
11424,
11436,
11444,
11448,
11488,
11515,
11535,
11555,
11616,
11622,
11664,
11676,
11688,
11711,
11824,
11832,
11848,
11872,
11888,
11916,
12112,
12122,
12124,
12126,
12128,
12132,
12144,
12162,
12168,
12184,
12212,
12216,
12222,
12224,
12244,
12248,
12264,
12288,
12312,
12324,
12336,
12366,
12384,
12412,
12424,
12432,
12444,
12448,
12488,
12492,
12612,
12624,
12636,
12648,
12666,
12712,
12726,
12768,
12816,
12824,
12848,
12864,
12888,
12924,
12996,
13113,
13116,
13122,
13128,
13131,
13155,
13164,
13212,
13224,
13236,
13248,
13266,
13272,
13311,
13326,
13332,
13335,
13344,
13362,
13368,
13377,
13392,
13416,
13464,
13488,
13515,
13626,
13632,
13644,
13662,
13713,
13755,
13776,
13797,
13824,
13848,
13896,
13932,
13968,
13995,
14112,
14124,
14128,
14136,
14144,
14184,
14212,
14224,
14232,
14244,
14248,
14288,
14292,
14316,
14328,
14364,
14412,
14424,
14436,
14444,
14448,
14488,
14616,
14664,
14688,
14728,
14784,
14824,
14832,
14848,
14888,
15115,
15135,
15155,
15315,
15515,
15555,
15575,
15715,
16116,
16122,
16128,
16164,
16212,
16224,
16236,
16248,
16266,
16326,
16332,
16344,
16362,
16368,
16416,
16464,
16488,
16626,
16632,
16644,
16662,
16716,
16824,
16848,
16992,
17115,
17122,
17136,
17171,
17199,
17248,
17262,
17444,
17472,
17535,
17717,
17724,
17766,
17955,
18112,
18128,
18144,
18168,
18184,
18216,
18224,
18248,
18264,
18288,
18312,
18336,
18384,
18424,
18432,
18448,
18488,
18624,
18648,
18816,
18824,
18848,
18864,
18872,
18888,
18936,
19116,
19224,
19296,
19332,
19368,
19395,
19692,
19719,
19926,
19935,
19944,
19962,
19971,
21112,
21122,
21124,
21126,
21128,
21132,
21144,
21162.
Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 1378948 values, from 1 to 499999968).
n\r | 0 | 1 |
2 | 1359183 | 19765 | 2 |
3 | 1312927 | 32984 | 33037 | 3 |
4 | 1299128 | 3055 | 60055 | 16710 | 4 |
5 | 13086 | 320476 | 326342 | 319476 | 399568 | 5 |
6 | 1293979 | 394 | 32614 | 18948 | 32590 | 423 | 6 |
7 | 455259 | 153917 | 153964 | 153965 | 154004 | 153980 | 153859 | 7 |
8 | 1047083 | 1654 | 30067 | 10227 | 252045 | 1401 | 29988 | 6483 | 8 |
9 | 786729 | 10968 | 11064 | 263012 | 10962 | 11022 | 263186 | 11054 | 10951 | 9 |
10 | 0 | 2011 | 325192 | 1904 | 397954 | 13086 | 318465 | 1150 | 317572 | 1614 | 10 |
11 | 125427 | 126271 | 126634 | 124036 | 126192 | 124896 | 125680 | 125925 | 125098 | 124338 | 124451 |
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.