A figurate number of the form n3. more
The first 600 cubic numbers :
1,
8,
27,
64,
125,
216,
343,
512,
729,
1000,
1331,
1728,
2197,
2744,
3375,
4096,
4913,
5832,
6859,
8000,
9261,
10648,
12167,
13824,
15625,
17576,
19683,
21952,
24389,
27000,
29791,
32768,
35937,
39304,
42875,
46656,
50653,
54872,
59319,
64000,
68921,
74088,
79507,
85184,
91125,
97336,
103823,
110592,
117649,
125000,
132651,
140608,
148877,
157464,
166375,
175616,
185193,
195112,
205379,
216000,
226981,
238328,
250047,
262144,
274625,
287496,
300763,
314432,
328509,
343000,
357911,
373248,
389017,
405224,
421875,
438976,
456533,
474552,
493039,
512000,
531441,
551368,
571787,
592704,
614125,
636056,
658503,
681472,
704969,
729000,
753571,
778688,
804357,
830584,
857375,
884736,
912673,
941192,
970299,
1000000,
1030301,
1061208,
1092727,
1124864,
1157625,
1191016,
1225043,
1259712,
1295029,
1331000,
1367631,
1404928,
1442897,
1481544,
1520875,
1560896,
1601613,
1643032,
1685159,
1728000,
1771561,
1815848,
1860867,
1906624,
1953125,
2000376,
2048383,
2097152,
2146689,
2197000,
2248091,
2299968,
2352637,
2406104,
2460375,
2515456,
2571353,
2628072,
2685619,
2744000,
2803221,
2863288,
2924207,
2985984,
3048625,
3112136,
3176523,
3241792,
3307949,
3375000,
3442951,
3511808,
3581577,
3652264,
3723875,
3796416,
3869893,
3944312,
4019679,
4096000,
4173281,
4251528,
4330747,
4410944,
4492125,
4574296,
4657463,
4741632,
4826809,
4913000,
5000211,
5088448,
5177717,
5268024,
5359375,
5451776,
5545233,
5639752,
5735339,
5832000,
5929741,
6028568,
6128487,
6229504,
6331625,
6434856,
6539203,
6644672,
6751269,
6859000,
6967871,
7077888,
7189057,
7301384,
7414875,
7529536,
7645373,
7762392,
7880599,
8000000,
8120601,
8242408,
8365427,
8489664,
8615125,
8741816,
8869743,
8998912,
9129329,
9261000,
9393931,
9528128,
9663597,
9800344,
9938375,
10077696,
10218313,
10360232,
10503459,
10648000,
10793861,
10941048,
11089567,
11239424,
11390625,
11543176,
11697083,
11852352,
12008989,
12167000,
12326391,
12487168,
12649337,
12812904,
12977875,
13144256,
13312053,
13481272,
13651919,
13824000,
13997521,
14172488,
14348907,
14526784,
14706125,
14886936,
15069223,
15252992,
15438249,
15625000,
15813251,
16003008,
16194277,
16387064,
16581375,
16777216,
16974593,
17173512,
17373979,
17576000,
17779581,
17984728,
18191447,
18399744,
18609625,
18821096,
19034163,
19248832,
19465109,
19683000,
19902511,
20123648,
20346417,
20570824,
20796875,
21024576,
21253933,
21484952,
21717639,
21952000,
22188041,
22425768,
22665187,
22906304,
23149125,
23393656,
23639903,
23887872,
24137569,
24389000,
24642171,
24897088,
25153757,
25412184,
25672375,
25934336,
26198073,
26463592,
26730899,
27000000,
27270901,
27543608,
27818127,
28094464,
28372625,
28652616,
28934443,
29218112,
29503629,
29791000,
30080231,
30371328,
30664297,
30959144,
31255875,
31554496,
31855013,
32157432,
32461759,
32768000,
33076161,
33386248,
33698267,
34012224,
34328125,
34645976,
34965783,
35287552,
35611289,
35937000,
36264691,
36594368,
36926037,
37259704,
37595375,
37933056,
38272753,
38614472,
38958219,
39304000,
39651821,
40001688,
40353607,
40707584,
41063625,
41421736,
41781923,
42144192,
42508549,
42875000,
43243551,
43614208,
43986977,
44361864,
44738875,
45118016,
45499293,
45882712,
46268279,
46656000,
47045881,
47437928,
47832147,
48228544,
48627125,
49027896,
49430863,
49836032,
50243409,
50653000,
51064811,
51478848,
51895117,
52313624,
52734375,
53157376,
53582633,
54010152,
54439939,
54872000,
55306341,
55742968,
56181887,
56623104,
57066625,
57512456,
57960603,
58411072,
58863869,
59319000,
59776471,
60236288,
60698457,
61162984,
61629875,
62099136,
62570773,
63044792,
63521199,
64000000,
64481201,
64964808,
65450827,
65939264,
66430125,
66923416,
67419143,
67917312,
68417929,
68921000,
69426531,
69934528,
70444997,
70957944,
71473375,
71991296,
72511713,
73034632,
73560059,
74088000,
74618461,
75151448,
75686967,
76225024,
76765625,
77308776,
77854483,
78402752,
78953589,
79507000,
80062991,
80621568,
81182737,
81746504,
82312875,
82881856,
83453453,
84027672,
84604519,
85184000,
85766121,
86350888,
86938307,
87528384,
88121125,
88716536,
89314623,
89915392,
90518849,
91125000,
91733851,
92345408,
92959677,
93576664,
94196375,
94818816,
95443993,
96071912,
96702579,
97336000,
97972181,
98611128,
99252847,
99897344,
100544625,
101194696,
101847563,
102503232,
103161709,
103823000,
104487111,
105154048,
105823817,
106496424,
107171875,
107850176,
108531333,
109215352,
109902239,
110592000,
111284641,
111980168,
112678587,
113379904,
114084125,
114791256,
115501303,
116214272,
116930169,
117649000,
118370771,
119095488,
119823157,
120553784,
121287375,
122023936,
122763473,
123505992,
124251499,
125000000,
125751501,
126506008,
127263527,
128024064,
128787625,
129554216,
130323843,
131096512,
131872229,
132651000,
133432831,
134217728,
135005697,
135796744,
136590875,
137388096,
138188413,
138991832,
139798359,
140608000,
141420761,
142236648,
143055667,
143877824,
144703125,
145531576,
146363183,
147197952,
148035889,
148877000,
149721291,
150568768,
151419437,
152273304,
153130375,
153990656,
154854153,
155720872,
156590819,
157464000,
158340421,
159220088,
160103007,
160989184,
161878625,
162771336,
163667323,
164566592,
165469149,
166375000,
167284151,
168196608,
169112377,
170031464,
170953875,
171879616,
172808693,
173741112,
174676879,
175616000,
176558481,
177504328,
178453547,
179406144,
180362125,
181321496,
182284263,
183250432,
184220009,
185193000,
186169411,
187149248,
188132517,
189119224,
190109375,
191102976,
192100033,
193100552,
194104539,
195112000,
196122941,
197137368,
198155287,
199176704,
200201625,
201230056,
202262003,
203297472,
204336469,
205379000,
206425071,
207474688,
208527857,
209584584,
210644875,
211708736,
212776173,
213847192,
214921799,
216000000.
Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 100000 values, from 1 to 1000000000000000).
n\r | 0 | 1 |
2 | 50000 | 50000 | 2 |
3 | 33333 | 33334 | 33333 | 3 |
4 | 50000 | 25000 | 0 | 25000 | 4 |
5 | 20000 | 20000 | 20000 | 20000 | 20000 | 5 |
6 | 16666 | 16667 | 16667 | 16667 | 16667 | 16666 | 6 |
7 | 14285 | 42858 | 0 | 0 | 0 | 0 | 42857 | 7 |
8 | 50000 | 12500 | 0 | 12500 | 0 | 12500 | 0 | 12500 | 8 |
9 | 33333 | 33334 | 0 | 0 | 0 | 0 | 0 | 0 | 33333 | 9 |
10 | 10000 | 10000 | 10000 | 10000 | 10000 | 10000 | 10000 | 10000 | 10000 | 10000 | 10 |
11 | 9090 | 9091 | 9091 | 9091 | 9091 | 9091 | 9091 | 9091 | 9091 | 9091 | 9091 |
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.