A composite whose sum of digits is equal to the sum of digits of its prime factors. more
The first 600 Smith numbers :
4,
22,
27,
58,
85,
94,
121,
166,
202,
265,
274,
319,
346,
355,
378,
382,
391,
438,
454,
483,
517,
526,
535,
562,
576,
588,
627,
634,
636,
645,
648,
654,
663,
666,
690,
706,
728,
729,
762,
778,
825,
852,
861,
895,
913,
915,
922,
958,
985,
1086,
1111,
1165,
1219,
1255,
1282,
1284,
1376,
1449,
1507,
1581,
1626,
1633,
1642,
1678,
1736,
1755,
1776,
1795,
1822,
1842,
1858,
1872,
1881,
1894,
1903,
1908,
1921,
1935,
1952,
1962,
1966,
2038,
2067,
2079,
2155,
2173,
2182,
2218,
2227,
2265,
2286,
2326,
2362,
2366,
2373,
2409,
2434,
2461,
2475,
2484,
2515,
2556,
2576,
2578,
2583,
2605,
2614,
2679,
2688,
2722,
2745,
2751,
2785,
2839,
2888,
2902,
2911,
2934,
2944,
2958,
2964,
2965,
2970,
2974,
3046,
3091,
3138,
3168,
3174,
3226,
3246,
3258,
3294,
3345,
3366,
3390,
3442,
3505,
3564,
3595,
3615,
3622,
3649,
3663,
3690,
3694,
3802,
3852,
3864,
3865,
3930,
3946,
3973,
4054,
4126,
4162,
4173,
4185,
4189,
4191,
4198,
4209,
4279,
4306,
4369,
4414,
4428,
4464,
4472,
4557,
4592,
4594,
4702,
4743,
4765,
4788,
4794,
4832,
4855,
4880,
4918,
4954,
4959,
4960,
4974,
4981,
5062,
5071,
5088,
5098,
5172,
5242,
5248,
5253,
5269,
5298,
5305,
5386,
5388,
5397,
5422,
5458,
5485,
5526,
5539,
5602,
5638,
5642,
5674,
5772,
5818,
5854,
5874,
5915,
5926,
5935,
5936,
5946,
5998,
6036,
6054,
6084,
6096,
6115,
6171,
6178,
6187,
6188,
6252,
6259,
6295,
6315,
6344,
6385,
6439,
6457,
6502,
6531,
6567,
6583,
6585,
6603,
6684,
6693,
6702,
6718,
6760,
6816,
6835,
6855,
6880,
6934,
6981,
7026,
7051,
7062,
7068,
7078,
7089,
7119,
7136,
7186,
7195,
7227,
7249,
7287,
7339,
7402,
7438,
7447,
7465,
7503,
7627,
7674,
7683,
7695,
7712,
7726,
7762,
7764,
7782,
7784,
7809,
7824,
7834,
7915,
7952,
7978,
8005,
8014,
8023,
8073,
8077,
8095,
8149,
8154,
8158,
8185,
8196,
8253,
8257,
8277,
8307,
8347,
8372,
8412,
8421,
8466,
8518,
8545,
8568,
8628,
8653,
8680,
8736,
8754,
8766,
8790,
8792,
8851,
8864,
8874,
8883,
8901,
8914,
9015,
9031,
9036,
9094,
9166,
9184,
9193,
9229,
9274,
9276,
9285,
9294,
9296,
9301,
9330,
9346,
9355,
9382,
9386,
9387,
9396,
9414,
9427,
9483,
9522,
9535,
9571,
9598,
9633,
9634,
9639,
9648,
9657,
9684,
9708,
9717,
9735,
9742,
9760,
9778,
9840,
9843,
9849,
9861,
9880,
9895,
9924,
9942,
9968,
9975,
9985,
10086,
10201,
10291,
10296,
10419,
10462,
10489,
10494,
10579,
10592,
10606,
10664,
10669,
10689,
10698,
10705,
10736,
10761,
10786,
10791,
10797,
10806,
10845,
10887,
10966,
11065,
11209,
11358,
11385,
11388,
11583,
11659,
11679,
11686,
11695,
11696,
11739,
11785,
11790,
11816,
11857,
11965,
11984,
12055,
12091,
12226,
12262,
12318,
12406,
12442,
12519,
12558,
12573,
12622,
12627,
12648,
12656,
12658,
12667,
12675,
12684,
12732,
12771,
12795,
12847,
12937,
12939,
12946,
12955,
12957,
12975,
12982,
13369,
13454,
13472,
13506,
13639,
13662,
13666,
13747,
13764,
13765,
13812,
13905,
13974,
13984,
14017,
14026,
14046,
14058,
14085,
14148,
14168,
14179,
14206,
14242,
14359,
14386,
14391,
14422,
14458,
14464,
14494,
14508,
14534,
14566,
14672,
14688,
14719,
14736,
14756,
14784,
14809,
14832,
14881,
14924,
14946,
14958,
14962,
14985,
14991,
14998,
15018,
15115,
15126,
15128,
15205,
15286,
15369,
15516,
15529,
15558,
15646,
15682,
15687,
15704,
15709,
15747,
15778,
15824,
15835,
15848,
15853,
15860,
15882,
15884,
15894,
15898,
15943,
15974,
15981,
15984,
16015,
16078,
16098,
16105,
16123,
16137,
16186,
16192,
16222,
16269,
16285,
16294,
16335,
16357,
16438,
16474,
16480,
16536,
16537,
16546,
16568,
16582,
16591,
16592,
16645,
16647,
16653,
16688,
16726,
16735,
16744,
16746,
16770,
16866,
16890,
16902,
16940,
16983,
17056,
17086,
17149,
17187,
17199,
17221,
17238,
17268,
17271,
17424,
17455,
17482,
17496,
17635,
17646,
17662,
17664,
17698,
17718,
17738,
17754,
17826,
17833,
17835,
17838,
17840,
17864,
17885,
17889,
17905,
17907,
17916,
17940,
17982.
Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 2632758 values, from 4 to 99999920).
n\r | 0 | 1 |
2 | 1488268 | 1144490 | 2 |
3 | 1167283 | 933780 | 531695 | 3 |
4 | 717559 | 568792 | 770709 | 575698 | 4 |
5 | 567656 | 508452 | 513626 | 526414 | 516610 | 5 |
6 | 588865 | 440152 | 405775 | 578418 | 493628 | 125920 | 6 |
7 | 435002 | 366587 | 365290 | 366800 | 366476 | 366419 | 366184 | 7 |
8 | 425436 | 285486 | 384670 | 287549 | 292123 | 283306 | 386039 | 288149 | 8 |
9 | 380972 | 94788 | 159416 | 285768 | 762255 | 125397 | 500543 | 76737 | 246882 | 9 |
10 | 251231 | 191543 | 290373 | 200838 | 304179 | 316425 | 316909 | 223253 | 325576 | 212431 | 10 |
11 | 277762 | 233653 | 235100 | 236189 | 236322 | 234325 | 236202 | 236672 | 235735 | 234647 | 236151 |
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.