A composite number the sum of whose digits is equal to the sum of the digits of its distinct prime factors. more
The first 600 hoax numbers :
22,
58,
84,
85,
94,
136,
160,
166,
202,
234,
250,
265,
274,
308,
319,
336,
346,
355,
361,
364,
382,
391,
424,
438,
454,
456,
476,
483,
516,
517,
526,
535,
562,
627,
634,
644,
645,
650,
654,
660,
663,
690,
702,
706,
732,
735,
762,
778,
855,
860,
861,
895,
913,
915,
922,
948,
958,
985,
1086,
1111,
1116,
1148,
1165,
1219,
1255,
1282,
1312,
1344,
1404,
1484,
1507,
1550,
1576,
1581,
1600,
1612,
1626,
1633,
1642,
1650,
1665,
1678,
1708,
1752,
1795,
1812,
1822,
1824,
1842,
1858,
1876,
1894,
1903,
1921,
1924,
1966,
2008,
2038,
2064,
2067,
2106,
2155,
2166,
2173,
2182,
2218,
2227,
2232,
2236,
2265,
2275,
2325,
2326,
2352,
2356,
2362,
2373,
2401,
2409,
2434,
2461,
2500,
2515,
2541,
2565,
2578,
2605,
2614,
2616,
2625,
2640,
2679,
2722,
2751,
2760,
2785,
2826,
2839,
2872,
2902,
2911,
2924,
2958,
2960,
2965,
2974,
3036,
3042,
3046,
3048,
3091,
3138,
3164,
3172,
3226,
3246,
3268,
3285,
3339,
3344,
3345,
3381,
3390,
3393,
3442,
3474,
3476,
3484,
3505,
3552,
3556,
3592,
3595,
3615,
3618,
3622,
3625,
3630,
3649,
3694,
3712,
3736,
3792,
3802,
3836,
3850,
3865,
3892,
3912,
3920,
3930,
3933,
3946,
3973,
4024,
4054,
4116,
4126,
4148,
4160,
4162,
4173,
4188,
4189,
4191,
4198,
4209,
4212,
4228,
4235,
4268,
4275,
4279,
4306,
4344,
4369,
4396,
4414,
4456,
4460,
4473,
4564,
4590,
4594,
4636,
4656,
4676,
4702,
4744,
4765,
4770,
4776,
4794,
4820,
4824,
4844,
4855,
4905,
4918,
4920,
4954,
4974,
4980,
4981,
5022,
5052,
5062,
5068,
5071,
5094,
5098,
5145,
5150,
5168,
5176,
5242,
5253,
5268,
5269,
5298,
5305,
5332,
5344,
5348,
5386,
5397,
5412,
5422,
5425,
5458,
5464,
5484,
5485,
5525,
5539,
5548,
5602,
5612,
5638,
5642,
5652,
5674,
5715,
5742,
5752,
5818,
5840,
5854,
5874,
5926,
5935,
5946,
5998,
6016,
6027,
6054,
6060,
6066,
6115,
6175,
6178,
6184,
6187,
6244,
6259,
6260,
6295,
6315,
6356,
6364,
6385,
6390,
6439,
6457,
6472,
6475,
6500,
6502,
6504,
6512,
6524,
6531,
6564,
6567,
6583,
6585,
6596,
6600,
6603,
6604,
6616,
6620,
6633,
6692,
6693,
6702,
6714,
6718,
6741,
6835,
6855,
6900,
6904,
6934,
6950,
6960,
6980,
6981,
7008,
7026,
7028,
7038,
7048,
7051,
7052,
7062,
7076,
7078,
7089,
7150,
7186,
7195,
7196,
7212,
7228,
7236,
7249,
7268,
7287,
7335,
7339,
7362,
7364,
7402,
7428,
7438,
7447,
7465,
7503,
7506,
7525,
7624,
7627,
7650,
7674,
7683,
7726,
7756,
7762,
7782,
7809,
7834,
7850,
7915,
7924,
7978,
8005,
8014,
8023,
8076,
8077,
8084,
8091,
8095,
8145,
8149,
8158,
8164,
8185,
8214,
8224,
8244,
8257,
8277,
8284,
8292,
8308,
8325,
8334,
8347,
8415,
8420,
8421,
8466,
8508,
8518,
8545,
8600,
8653,
8673,
8720,
8724,
8754,
8780,
8790,
8816,
8851,
8914,
8924,
8932,
8955,
8982,
9015,
9028,
9031,
9052,
9094,
9096,
9116,
9166,
9180,
9193,
9229,
9274,
9285,
9294,
9301,
9306,
9330,
9333,
9346,
9350,
9355,
9382,
9412,
9425,
9427,
9436,
9483,
9528,
9535,
9540,
9571,
9598,
9630,
9634,
9650,
9652,
9711,
9716,
9717,
9735,
9742,
9772,
9778,
9843,
9861,
9895,
9916,
9940,
9942,
9985,
10044,
10075,
10179,
10188,
10192,
10240,
10268,
10278,
10291,
10375,
10392,
10406,
10419,
10462,
10464,
10489,
10492,
10550,
10560,
10579,
10604,
10606,
10624,
10669,
10675,
10689,
10698,
10704,
10705,
10761,
10780,
10786,
10797,
10806,
10854,
10884,
10887,
10926,
10936,
10948,
10966,
10982,
11065,
11124,
11209,
11228,
11232,
11468,
11476,
11484,
11574,
11659,
11679,
11686,
11688,
11695,
11712,
11739,
11774,
11775,
11785,
11857,
11908,
11913,
11944,
11965,
12055,
12068,
12091,
12144,
12188,
12192,
12195,
12226,
12256,
12262,
12318,
12366,
12388,
12406,
12442,
12464,
12532,
12546,
12552,
12556,
12558,
12612,
12622,
12650,
12658,
12664,
12667,
12775,
12780,
12795,
12796,
12825,
12828,
12847,
12880,
12908,
12932,
12937,
12939,
12946,
12952,
12955.
Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 3183722 values, from 22 to 99999706).
n\r | 0 | 1 |
2 | 1948769 | 1234953 | 2 |
3 | 1233009 | 1329241 | 621472 | 3 |
4 | 1129882 | 621021 | 818887 | 613932 | 4 |
5 | 750173 | 606093 | 612876 | 604463 | 610117 | 5 |
6 | 647456 | 507113 | 479185 | 585553 | 822128 | 142287 | 6 |
7 | 470992 | 452351 | 451693 | 452593 | 451898 | 452433 | 451762 | 7 |
8 | 391426 | 310883 | 410090 | 307432 | 738456 | 310138 | 408797 | 306500 | 8 |
9 | 405665 | 242918 | 213014 | 290956 | 880136 | 192067 | 536388 | 206187 | 216391 | 9 |
10 | 352804 | 204470 | 392520 | 208801 | 406160 | 397369 | 401623 | 220356 | 395662 | 203957 | 10 |
11 | 282880 | 288848 | 289077 | 290998 | 290672 | 289681 | 290145 | 291525 | 290357 | 289508 | 290031 |
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.