Search a number
droll numbers
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 
219810 2 
31385291305 3 
41981000 4 
51129197185249221 5 
61385030502910 6 
7942202174143208141171 7 
819810000000 8 
99561101042248011620510185 9 
10112901850221019702490 10 
11675132128133135123138123141127126

A pictorial representation of the table above
motab
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.