A number whose even prime factors and odd prime factors have the same sum. more
The first 600 droll numbers :
72,
240,
672,
800,
2240,
4224,
5184,
6272,
9984,
14080,
17280,
33280,
39424,
48384,
52224,
57600,
93184,
116736,
161280,
174080,
192000,
247808,
304128,
373248,
389120,
451584,
487424,
537600,
565248,
585728,
640000,
718848,
1013760,
1089536,
1244160,
1384448,
1505280,
1792000,
1884160,
2396160,
2838528,
3063808,
3379200,
3483648,
3760128,
4147200,
4214784,
5017600,
5275648,
5701632,
6709248,
6848512,
7241728,
7987200,
8404992,
9461760,
11264000,
11612160,
12189696,
12533760,
13824000,
14049280,
16187392,
17842176,
19005440,
21897216,
22364160,
26492928,
26624000,
26873856,
28016640,
31539200,
32514048,
33161216,
35094528,
37879808,
38707200,
39337984,
40632320,
40697856,
41779200,
42172416,
46080000,
51757056,
53215232,
59473920,
62619648,
72990720,
74547200,
78381056,
78446592,
84672512,
88309760,
89579520,
93388800,
99680256,
108380160,
113770496,
116391936,
116981760,
129024000,
135659520,
139264000,
140574720,
153600000,
166526976,
172523520,
189267968,
198246400,
204374016,
208732160,
220594176,
243302400,
247267328,
250822656,
261488640,
270729216,
298598400,
303464448,
311296000,
327548928,
332267520,
334495744,
361267200,
379846656,
387973120,
389939200,
393609216,
409993216,
410517504,
430080000,
452198400,
468582400,
483065856,
493092864,
512000000,
515899392,
521404416,
555089920,
575078400,
584450048,
605159424,
681246720,
715128832,
732168192,
735313920,
790626304,
811008000,
836075520,
871628800,
877658112,
902430720,
916455424,
930349056,
995328000,
1011548160,
1046740992,
1082130432,
1086324736,
1091829760,
1107558400,
1165492224,
1204224000,
1266155520,
1284636672,
1312030720,
1368391680,
1433600000,
1507328000,
1554251776,
1576599552,
1610219520,
1643642880,
1690304512,
1719664640,
1738014720,
1907490816,
1916928000,
1934917632,
2017198080,
2058878976,
2270822400,
2341011456,
2387607552,
2440560640,
2451046400,
2474115072,
2526806016,
2703360000,
2727346176,
2786918400,
2832334848,
2925527040,
2930245632,
3008102400,
3036413952,
3057123328,
3101163520,
3317760000,
3371827200,
3489136640,
3545235456,
3607101440,
3673686016,
3726508032,
3831496704,
3884974080,
4014080000,
4135583744,
4220518400,
4282122240,
4437573632,
4508614656,
4561305600,
4602200064,
4731174912,
4815060992,
4866441216,
5255331840,
5367398400,
5478809600,
5643436032,
5648154624,
5793382400,
5847908352,
6096420864,
6358302720,
6389760000,
6449725440,
6723993600,
6828326912,
6833569792,
6862929920,
7176978432,
7569408000,
7803371520,
7958691840,
8191475712,
8247050240,
8380219392,
8422686720,
8683257856,
8841592832,
9011200000,
9091153920,
9244246016,
9289728000,
9441116160,
9751756800,
9767485440,
9769582592,
10027008000,
10099884032,
10121379840,
10877927424,
11059200000,
11239424000,
11817451520,
11989942272,
12421693440,
12771655680,
12941524992,
12949913600,
13627293696,
13822328832,
14273740800,
14714929152,
15028715520,
15204352000,
15340666880,
15770583040,
15882780672,
16139681792,
16221470720,
17517772800,
17803247616,
17891328000,
18059231232,
18811453440,
18827182080,
19216203776,
19492503552,
19493027840,
19763560448,
20321402880,
21194342400,
21299200000,
21499084800,
21849440256,
22284337152,
22413312000,
23091740672,
23583522816,
23923261440,
24083693568,
25231360000,
25455230976,
26011238400,
26435125248,
26528972800,
27304919040,
27348959232,
27934064640,
28075622400,
28339863552,
28928114688,
29519511552,
29557260288,
30266097664,
30303846400,
30589059072,
30965760000,
31470387200,
32505856000,
32558284800,
33088864256,
33423360000,
33737932800,
34780741632,
35502686208,
35760635904,
36259758080,
36864000000,
37144756224,
37541117952,
39966474240,
41405644800,
42080403456,
42572185600,
42681237504,
42953867264,
43138416640,
43571478528,
44157632512,
44761612288,
45420118016,
45424312320,
46074429440,
47579136000,
49049763840,
50095718400,
51489275904,
52672069632,
52716109824,
52942602240,
54580477952,
56899928064,
56925093888,
58392576000,
59344158720,
59637760000,
60197437440,
61408804864,
62704844800,
62757273600,
63191384064,
63484985344,
64975011840,
65984790528,
66985132032,
67738009600,
68375543808,
70647808000,
71538049024,
71663616000,
72301412352,
72831467520,
74281123840,
74711040000,
75365351424,
76453773312,
77913391104,
78215380992,
78611742720,
79744204800,
80278978560,
83915440128,
84422950912,
84850769920,
86704128000,
88117084160,
91016396800,
91163197440,
92493840384,
93113548800,
93585408000,
94466211840,
95697240064,
96427048960,
98398371840,
98524200960,
101527322624,
101963530240,
103219200000,
108527616000,
111411200000,
111906127872,
112459776000,
113515167744,
115935805440,
118342287360,
119202119680,
120787566592,
121701924864,
122880000000,
123815854080,
125137059840,
127188074496,
129008402432,
133221580800,
137339338752,
138018816000,
139314069504,
140072976384,
140268011520,
142270791680,
145148084224,
145238261760,
148239286272,
150055419904,
151414374400,
158597120000,
160004308992,
161614921728,
163499212800,
166163644416,
166985728000,
168552824832,
171630919680,
171907743744,
175573565440,
175720366080,
176475340800,
178136285184,
181930033152,
188710125568,
189666426880,
189750312960,
194641920000,
196368924672,
197813862400,
200658124800,
203928109056,
207987146752,
209190912000,
210637946880,
210977685504,
216583372800,
218621804544,
219949301760,
220112879616,
223283773440,
224781139968,
227918479360,
237582155776,
238878720000,
241004707840,
242771558400,
246727835648,
249036800000,
251217838080,
254845911040,
255256952832,
259711303680,
260717936640,
262039142400,
264505393152,
265814016000,
267596595200,
268308578304,
269995737088,
275515441152,
275867762688,
277562261504,
279718133760,
285497884672,
289013760000,
297762029568,
303877324800,
308312801280,
310378496000,
311951360000,
314887372800,
319505301504,
324620255232,
327994572800,
328414003200,
331081580544,
331358404608,
333765935104,
340644593664,
343077289984,
344064000000,
346684391424,
350383767552,
357656690688,
361758720000,
373020426240,
374199025664,
374865920000,
378192003072,
378383892480,
380104605696,
386452684800,
392750432256,
394474291200,
398358216704,
405673082880,
406327394304,
406667132928,
409600000000,
412719513600,
417123532800,
421049401344,
423960248320,
438942302208,
444071936000,
451508436992,
457797795840,
460062720000,
464380231680,
466909921280,
467560038400,
480566575104,
484127539200,
491605983232,
491639537664,
492017025024,
494130954240,
516742447104,
531065995264,
531300876288,
533347696640,
538716405760,
544997376000,
553878814720,
561842749440,
572103065600,
573025812480,
585734553600,
588251136000,
589786251264,
593787617280,
603375796224,
606433443840,
615858044928,
625194565632,
632501043200,
636594683904,
638171742208,
648806400000,
654563082240,
656056254464,
665585713152,
668860416000,
674813181952,
679760363520,
697303040000,
702126489600,
703258951680,
703409946624,
713568550912,
721944576000,
727191650304,
728739348480,
730010222592,
733164339200,
733709598720,
744279244800,
749270466560,
759236132864,
782556463104,
783210774528,
784905273344,
785979015168,
796262400000,
799467896832,
809238528000,
810909958144,
836444880896,
837392793600,
845370359808,
850856509440,
863275843584,
865704345600,
869059788800,
873463808000,
881684643840,
886046720000,
894361927680,
913754292224,
918384803840,
919559208960,
931789799424,
932393779200,
963379200000,
965293899776,
981165146112,
992540098560,
995207675904.
Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 1981 values, from 72 to 998511176843264).
n\r | 0 | 1 |
2 | 1981 | 0 | 2 |
3 | 1385 | 291 | 305 | 3 |
4 | 1981 | 0 | 0 | 0 | 4 |
5 | 1129 | 197 | 185 | 249 | 221 | 5 |
6 | 1385 | 0 | 305 | 0 | 291 | 0 | 6 |
7 | 942 | 202 | 174 | 143 | 208 | 141 | 171 | 7 |
8 | 1981 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 8 |
9 | 956 | 110 | 104 | 224 | 80 | 116 | 205 | 101 | 85 | 9 |
10 | 1129 | 0 | 185 | 0 | 221 | 0 | 197 | 0 | 249 | 0 | 10 |
11 | 675 | 132 | 128 | 133 | 135 | 123 | 138 | 123 | 141 | 127 | 126 |
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.