A number divisible by the sum of any subset of its (nonzero) digits. more
The first 600 super Niven numbers :
1,
2,
3,
4,
5,
6,
7,
8,
9,
10,
12,
20,
24,
30,
36,
40,
48,
50,
60,
70,
80,
90,
100,
102,
110,
120,
140,
150,
200,
204,
210,
220,
240,
280,
300,
306,
330,
360,
400,
408,
420,
440,
480,
500,
510,
540,
550,
600,
630,
660,
700,
770,
800,
840,
880,
900,
990,
1000,
1002,
1008,
1010,
1020,
1040,
1050,
1080,
1100,
1110,
1140,
1200,
1320,
1400,
1440,
1500,
1800,
2000,
2004,
2010,
2016,
2020,
2040,
2080,
2100,
2200,
2220,
2280,
2400,
2520,
2640,
2800,
2880,
3000,
3006,
3030,
3060,
3120,
3300,
3330,
3600,
3960,
4000,
4008,
4020,
4040,
4080,
4100,
4200,
4400,
4440,
4500,
4800,
5000,
5010,
5040,
5050,
5100,
5400,
5500,
5550,
6000,
6030,
6060,
6240,
6300,
6600,
6660,
7000,
7070,
7700,
7770,
8000,
8040,
8080,
8200,
8400,
8800,
8880,
9000,
9090,
9360,
9900,
9990,
10000,
10002,
10008,
10010,
10020,
10040,
10050,
10080,
10100,
10110,
10140,
10200,
10320,
10400,
10440,
10500,
10800,
11000,
11010,
11040,
11100,
11220,
11400,
12000,
12120,
12300,
12600,
13020,
13200,
14000,
14040,
14100,
14400,
15000,
15120,
18000,
20000,
20004,
20010,
20020,
20040,
20080,
20100,
20160,
20200,
20220,
20280,
20400,
20640,
20800,
20880,
21000,
21120,
21300,
22000,
22020,
22080,
22200,
22440,
22800,
23100,
24000,
24240,
24600,
25200,
26040,
26400,
28000,
28080,
28200,
28800,
30000,
30006,
30030,
30060,
30120,
30240,
30300,
30330,
30600,
30960,
31020,
31200,
32100,
33000,
33030,
33300,
33660,
34020,
36000,
36360,
36900,
39060,
39600,
40000,
40008,
40020,
40040,
40080,
40100,
40200,
40320,
40400,
40440,
40500,
40800,
41000,
41040,
41100,
41400,
42000,
42240,
42600,
44000,
44040,
44400,
44880,
45000,
46200,
48000,
48480,
50000,
50010,
50040,
50050,
50100,
50400,
50500,
50550,
51000,
52500,
54000,
55000,
55020,
55050,
55500,
60000,
60030,
60060,
60240,
60300,
60480,
60600,
60660,
62040,
62400,
63000,
63360,
63900,
64200,
66000,
66060,
66600,
68040,
69300,
70000,
70070,
70700,
70770,
77000,
77070,
77700,
80000,
80040,
80080,
80200,
80400,
80640,
80800,
80880,
81000,
82000,
82080,
82200,
82800,
84000,
84480,
88000,
88080,
88800,
90000,
90090,
90360,
90900,
90990,
91800,
93060,
93600,
96300,
99000,
99090,
99900,
100000,
100002,
100008,
100010,
100020,
100040,
100050,
100080,
100100,
100110,
100140,
100200,
100320,
100400,
100440,
100500,
100800,
101000,
101010,
101040,
101100,
101220,
101400,
101640,
102000,
102120,
102300,
103020,
103200,
103320,
104000,
104040,
104100,
104400,
105000,
108000,
110000,
110010,
110040,
110100,
110220,
110400,
111000,
111120,
111300,
112020,
112200,
113100,
113400,
114000,
115500,
120000,
120120,
120300,
121020,
121200,
122100,
123000,
126000,
130020,
130200,
131040,
131100,
132000,
135000,
140000,
140040,
140100,
140400,
141000,
141120,
144000,
150000,
151200,
153000,
180000,
200000,
200004,
200010,
200020,
200040,
200080,
200100,
200200,
200220,
200280,
200340,
200400,
200640,
200800,
200880,
201000,
201120,
201300,
201600,
202000,
202020,
202080,
202200,
202440,
202800,
203100,
204000,
204120,
204240,
204600,
206040,
206400,
206640,
208000,
208080,
208200,
208800,
210000,
210120,
210300,
211020,
211200,
212100,
213000,
214200,
220000,
220020,
220080,
220200,
220440,
220500,
220800,
221100,
222000,
222240,
222600,
223020,
224040,
224400,
226200,
226800,
228000,
230100,
231000,
240000,
240240,
240600,
242040,
242400,
244200,
246000,
252000,
260040,
260400,
262080,
262200,
264000,
277200,
280000,
280080,
280200,
280800,
282000,
282240,
288000,
300000,
300006,
300030,
300060,
300120,
300300,
300330,
300600,
300960,
301020,
301200,
302100,
302400,
303000,
303030,
303300,
303660,
306000,
306360,
306900,
309060,
309600,
309960,
310020,
310200,
311100,
312000,
315000,
320040,
320100,
321000,
330000,
330030,
330120,
330300,
330660,
333000,
333360,
333900,
336060,
336600,
339300,
340200,
351000,
357000,
360000,
360360,
360900,
363060,
363600,
366300,
369000,
390060,
390600,
393300,
396000,
400000,
400008,
400020,
400040,
400080,
400100,
400200,
400400,
400440,
400500,
400680,
400800,
401000,
401040,
401100,
401400,
402000,
402240,
402600,
403200,
404000,
404040,
404400,
404880,
405000,
406200,
408000,
408240,
408480,
409500,
410000,
410040,
410100,
410400,
411000,
414000,
420000,
420240,
420600,
422040,
422400,
424200,
426000,
428400,
440000,
440040,
440400,
440880,
441000,
442200.
Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 19944 values, from 1 to 48888000000).
n\r | 0 | 1 |
2 | 19939 | 5 | 2 |
3 | 19473 | 233 | 238 | 3 |
4 | 19681 | 3 | 258 | 2 | 4 |
5 | 19882 | 18 | 12 | 20 | 12 | 5 |
6 | 19471 | 2 | 237 | 2 | 231 | 1 | 6 |
7 | 8500 | 1908 | 1900 | 1908 | 1906 | 1915 | 1907 | 7 |
8 | 16914 | 2 | 147 | 1 | 2767 | 1 | 111 | 1 | 8 |
9 | 10246 | 120 | 56 | 3807 | 60 | 127 | 5420 | 53 | 55 | 9 |
10 | 19881 | 1 | 11 | 1 | 11 | 1 | 17 | 1 | 19 | 1 | 10 |
11 | 3594 | 1450 | 1699 | 1739 | 1792 | 1603 | 1629 | 1693 | 1779 | 1573 | 1393 |
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.