A number n such that there is not a k which divided by its sum of digits gives n. more
The first 600 inconsummate numbers :
62,
63,
65,
75,
84,
95,
161,
173,
195,
216,
261,
266,
272,
276,
326,
371,
372,
377,
381,
383,
386,
387,
395,
411,
416,
422,
426,
431,
432,
438,
441,
443,
461,
466,
471,
476,
482,
483,
486,
488,
491,
492,
493,
494,
497,
498,
516,
521,
522,
527,
531,
533,
536,
542,
543,
546,
549,
552,
553,
563,
564,
573,
575,
612,
615,
620,
623,
630,
635,
639,
645,
650,
675,
716,
723,
750,
761,
771,
776,
785,
795,
816,
821,
822,
827,
831,
834,
839,
840,
845,
861,
866,
872,
876,
882,
926,
927,
932,
933,
936,
938,
941,
942,
945,
950,
966,
971,
972,
983,
986,
993,
1016,
1026,
1037,
1038,
1041,
1043,
1046,
1049,
1052,
1053,
1076,
1082,
1086,
1107,
1161,
1166,
1173,
1175,
1266,
1271,
1272,
1316,
1326,
1371,
1376,
1382,
1416,
1437,
1481,
1482,
1487,
1488,
1491,
1493,
1494,
1496,
1497,
1499,
1521,
1526,
1527,
1532,
1533,
1536,
1538,
1541,
1542,
1553,
1566,
1571,
1572,
1586,
1593,
1596,
1598,
1599,
1601,
1602,
1604,
1605,
1610,
1616,
1626,
1631,
1632,
1641,
1643,
1646,
1649,
1652,
1653,
1656,
1673,
1716,
1730,
1745,
1811,
1826,
1866,
1871,
1872,
1895,
1926,
1931,
1932,
1950,
1971,
1976,
1982,
1983,
1986,
2016,
2037,
2042,
2043,
2046,
2049,
2052,
2076,
2082,
2093,
2126,
2144,
2147,
2148,
2153,
2156,
2160,
2177,
2181,
2207,
2214,
2217,
2261,
2271,
2276,
2316,
2372,
2376,
2382,
2426,
2477,
2481,
2511,
2526,
2537,
2544,
2547,
2555,
2577,
2588,
2591,
2592,
2594,
2597,
2598,
2601,
2603,
2604,
2606,
2609,
2610,
2616,
2631,
2642,
2643,
2646,
2649,
2652,
2660,
2672,
2676,
2682,
2705,
2706,
2709,
2712,
2715,
2720,
2726,
2742,
2753,
2756,
2760,
2811,
2816,
2826,
2877,
2888,
2911,
2921,
2922,
2937,
2961,
2966,
2972,
2976,
2982,
2993,
3026,
3037,
3038,
3041,
3042,
3046,
3053,
3083,
3086,
3093,
3107,
3111,
3116,
3126,
3137,
3144,
3147,
3149,
3152,
3153,
3156,
3177,
3186,
3207,
3218,
3221,
3222,
3237,
3247,
3248,
3251,
3254,
3255,
3257,
3258,
3260,
3263,
3281,
3287,
3288,
3291,
3294,
3296,
3307,
3311,
3314,
3317,
3318,
3321,
3324,
3327,
3329,
3332,
3371,
3372,
3383,
3386,
3416,
3426,
3437,
3444,
3477,
3482,
3483,
3486,
3537,
3548,
3551,
3554,
3555,
3581,
3587,
3588,
3591,
3593,
3621,
3627,
3644,
3647,
3648,
3651,
3654,
3657,
3658,
3659,
3661,
3662,
3665,
3666,
3677,
3681,
3687,
3692,
3696,
3697,
3698,
3699,
3701,
3702,
3703,
3704,
3705,
3706,
3707,
3708,
3710,
3711,
3712,
3713,
3714,
3716,
3717,
3719,
3720,
3722,
3726,
3731,
3732,
3733,
3738,
3741,
3743,
3744,
3746,
3747,
3749,
3752,
3753,
3755,
3756,
3758,
3759,
3761,
3762,
3764,
3765,
3767,
3768,
3770,
3771,
3773,
3776,
3782,
3783,
3786,
3787,
3788,
3791,
3792,
3793,
3794,
3796,
3797,
3798,
3801,
3803,
3804,
3805,
3806,
3809,
3810,
3812,
3813,
3815,
3816,
3818,
3819,
3821,
3822,
3824,
3825,
3827,
3828,
3830,
3831,
3836,
3838,
3842,
3843,
3846,
3849,
3852,
3854,
3855,
3857,
3860,
3863,
3864,
3866,
3867,
3869,
3870,
3872,
3873,
3875,
3876,
3878,
3879,
3882,
3926,
3927,
3932,
3933,
3936,
3938,
3941,
3942,
3945,
3950,
3966,
3971,
3972,
3983,
3986,
3993,
4016,
4026,
4037,
4038,
4041,
4043,
4046,
4049,
4052,
4053,
4076,
4077,
4082,
4086,
4088,
4091,
4092,
4094,
4097,
4098,
4099,
4101,
4103,
4104,
4106,
4109,
4110,
4116,
4121,
4122,
4127,
4131,
4142,
4143,
4146,
4149,
4151,
4152,
4154,
4155,
4157,
4160,
4164,
4165,
4172,
4176,
4182,
4183,
4187,
4188,
4191,
4193,
4194,
4196,
4197,
4198,
4199,
4202,
4203,
4205,
4206,
4208,
4209,
4212,
4215,
4219,
4220,
4226,
4227,
4232,
4233,
4236,
4238,
4241,
4242,
4246,
4253,
4256,
4260,
4262,
4263,
4264,
4265,
4266,
4268,
4269,
4271,
4272,
4273,
4275,
4283,
4286,
4293,
4298,
4299.
Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 183089 values, from 62 to 999995).
n\r | 0 | 1 |
2 | 93279 | 89810 | 2 |
3 | 89083 | 4700 | 89306 | 3 |
4 | 46368 | 46584 | 46911 | 43226 | 4 |
5 | 35485 | 34101 | 47318 | 30408 | 35777 | 5 |
6 | 45517 | 2595 | 45657 | 43566 | 2105 | 43649 | 6 |
7 | 26197 | 26151 | 26101 | 26203 | 26192 | 26150 | 26095 | 7 |
8 | 23201 | 23324 | 23591 | 21678 | 23167 | 23260 | 23320 | 21548 | 8 |
9 | 29658 | 2 | 29740 | 29709 | 2383 | 29774 | 29716 | 2315 | 29792 | 9 |
10 | 16430 | 17832 | 20404 | 11910 | 21678 | 19055 | 16269 | 26914 | 18498 | 14099 | 10 |
11 | 15821 | 16706 | 16278 | 17210 | 18921 | 13108 | 17158 | 19473 | 15035 | 16803 | 16576 |
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.