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constructible polygons
Numbers which count the sides of regular polygons constructible with ruler and compass. more

The first 600 constructible polygons :
3, 4, 5, 6, 8, 10, 12, 15, 16, 17, 20, 24, 30, 32, 34, 40, 48, 51, 60, 64, 68, 80, 85, 96, 102, 120, 128, 136, 160, 170, 192, 204, 240, 255, 256, 257, 272, 320, 340, 384, 408, 480, 510, 512, 514, 544, 640, 680, 768, 771, 816, 960, 1020, 1024, 1028, 1088, 1280, 1285, 1360, 1536, 1542, 1632, 1920, 2040, 2048, 2056, 2176, 2560, 2570, 2720, 3072, 3084, 3264, 3840, 3855, 4080, 4096, 4112, 4352, 4369, 5120, 5140, 5440, 6144, 6168, 6528, 7680, 7710, 8160, 8192, 8224, 8704, 8738, 10240, 10280, 10880, 12288, 12336, 13056, 13107, 15360, 15420, 16320, 16384, 16448, 17408, 17476, 20480, 20560, 21760, 21845, 24576, 24672, 26112, 26214, 30720, 30840, 32640, 32768, 32896, 34816, 34952, 40960, 41120, 43520, 43690, 49152, 49344, 52224, 52428, 61440, 61680, 65280, 65535, 65536, 65537, 65792, 69632, 69904, 81920, 82240, 87040, 87380, 98304, 98688, 104448, 104856, 122880, 123360, 130560, 131070, 131072, 131074, 131584, 139264, 139808, 163840, 164480, 174080, 174760, 196608, 196611, 197376, 208896, 209712, 245760, 246720, 261120, 262140, 262144, 262148, 263168, 278528, 279616, 327680, 327685, 328960, 348160, 349520, 393216, 393222, 394752, 417792, 419424, 491520, 493440, 522240, 524280, 524288, 524296, 526336, 557056, 559232, 655360, 655370, 657920, 696320, 699040, 786432, 786444, 789504, 835584, 838848, 983040, 983055, 986880, 1044480, 1048560, 1048576, 1048592, 1052672, 1114112, 1114129, 1118464, 1310720, 1310740, 1315840, 1392640, 1398080, 1572864, 1572888, 1579008, 1671168, 1677696, 1966080, 1966110, 1973760, 2088960, 2097120, 2097152, 2097184, 2105344, 2228224, 2228258, 2236928, 2621440, 2621480, 2631680, 2785280, 2796160, 3145728, 3145776, 3158016, 3342336, 3342387, 3355392, 3932160, 3932220, 3947520, 4177920, 4194240, 4194304, 4194368, 4210688, 4456448, 4456516, 4473856, 5242880, 5242960, 5263360, 5570560, 5570645, 5592320, 6291456, 6291552, 6316032, 6684672, 6684774, 6710784, 7864320, 7864440, 7895040, 8355840, 8388480, 8388608, 8388736, 8421376, 8912896, 8913032, 8947712, 10485760, 10485920, 10526720, 11141120, 11141290, 11184640, 12582912, 12583104, 12632064, 13369344, 13369548, 13421568, 15728640, 15728880, 15790080, 16711680, 16711935, 16776960, 16777216, 16777472, 16842752, 16843009, 17825792, 17826064, 17895424, 20971520, 20971840, 21053440, 22282240, 22282580, 22369280, 25165824, 25166208, 25264128, 26738688, 26739096, 26843136, 31457280, 31457760, 31580160, 33423360, 33423870, 33553920, 33554432, 33554944, 33685504, 33686018, 35651584, 35652128, 35790848, 41943040, 41943680, 42106880, 44564480, 44565160, 44738560, 50331648, 50332416, 50528256, 50529027, 53477376, 53478192, 53686272, 62914560, 62915520, 63160320, 66846720, 66847740, 67107840, 67108864, 67109888, 67371008, 67372036, 71303168, 71304256, 71581696, 83886080, 83887360, 84213760, 84215045, 89128960, 89130320, 89477120, 100663296, 100664832, 101056512, 101058054, 106954752, 106956384, 107372544, 125829120, 125831040, 126320640, 133693440, 133695480, 134215680, 134217728, 134219776, 134742016, 134744072, 142606336, 142608512, 143163392, 167772160, 167774720, 168427520, 168430090, 178257920, 178260640, 178954240, 201326592, 201329664, 202113024, 202116108, 213909504, 213912768, 214745088, 251658240, 251662080, 252641280, 252645135, 267386880, 267390960, 268431360, 268435456, 268439552, 269484032, 269488144, 285212672, 285217024, 286326784, 286331153, 335544320, 335549440, 336855040, 336860180, 356515840, 356521280, 357908480, 402653184, 402659328, 404226048, 404232216, 427819008, 427825536, 429490176, 503316480, 503324160, 505282560, 505290270, 534773760, 534781920, 536862720, 536870912, 536879104, 538968064, 538976288, 570425344, 570434048, 572653568, 572662306, 671088640, 671098880, 673710080, 673720360, 713031680, 713042560, 715816960, 805306368, 805318656, 808452096, 808464432, 855638016, 855651072, 858980352, 858993459, 1006632960, 1006648320, 1010565120, 1010580540, 1069547520, 1069563840, 1073725440, 1073741824, 1073758208, 1077936128, 1077952576, 1140850688, 1140868096, 1145307136, 1145324612, 1342177280, 1342197760, 1347420160, 1347440720, 1426063360, 1426085120, 1431633920, 1431655765, 1610612736, 1610637312, 1616904192, 1616928864, 1711276032, 1711302144, 1717960704, 1717986918, 2013265920, 2013296640, 2021130240, 2021161080, 2139095040, 2139127680, 2147450880, 2147483648, 2147516416, 2155872256, 2155905152, 2281701376, 2281736192, 2290614272, 2290649224, 2684354560, 2684395520, 2694840320, 2694881440, 2852126720, 2852170240, 2863267840, 2863311530, 3221225472, 3221274624, 3233808384, 3233857728, 3422552064, 3422604288, 3435921408, 3435973836, 4026531840, 4026593280, 4042260480, 4042322160, 4278190080, 4278255360, 4294901760, 4294967295, 4294967296, 4295032832, 4311744512, 4311810304, 4563402752, 4563472384, 4581228544, 4581298448, 5368709120, 5368791040, 5389680640, 5389762880, 5704253440, 5704340480, 5726535680, 5726623060, 6442450944, 6442549248, 6467616768, 6467715456, 6845104128, 6845208576, 6871842816, 6871947672, 8053063680, 8053186560, 8084520960, 8084644320, 8556380160, 8556510720, 8589803520, 8589934590, 8589934592, 8590065664, 8623489024, 8623620608, 9126805504, 9126944768, 9162457088, 9162596896, 10737418240, 10737582080, 10779361280, 10779525760, 11408506880, 11408680960, 11453071360, 11453246120, 12884901888, 12885098496, 12935233536, 12935430912, 13690208256, 13690417152, 13743685632, 13743895344, 16106127360, 16106373120, 16169041920, 16169288640, 17112760320, 17113021440, 17179607040, 17179869180, 17179869184, 17180131328, 17246978048, 17247241216, 18253611008, 18253889536, 18324914176, 18325193792, 21474836480, 21475164160.

Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 1094 values, from 3 to 900719925264384).

n\r 0  1 
2106331 2 
3536279279 3 
41032153116 4 
5528140142141143 5 
65207271162728 6 
70185183187178181180 7 
810007158328168 8 
90939126894942689294 9 
10512313621391613761394 10 
110110108109108111111108109109111

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.