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taxicab numbers
A number that can be written as a sum of two positive cubes in more than one way. more

The first 600 taxicab numbers :
1729, 4104, 13832, 20683, 32832, 39312, 40033, 46683, 64232, 65728, 110656, 110808, 134379, 149389, 165464, 171288, 195841, 216027, 216125, 262656, 314496, 320264, 327763, 373464, 402597, 439101, 443889, 513000, 513856, 515375, 525824, 558441, 593047, 684019, 704977, 805688, 842751, 885248, 886464, 920673, 955016, 984067, 994688, 1009736, 1016496, 1061424, 1073375, 1075032, 1080891, 1092728, 1195112, 1260441, 1323712, 1331064, 1370304, 1407672, 1533357, 1566728, 1609272, 1728216, 1729000, 1734264, 1774656, 1845649, 2048391, 2101248, 2301299, 2418271, 2515968, 2562112, 2585375, 2622104, 2691451, 2864288, 2987712, 2991816, 3220776, 3242197, 3375001, 3375008, 3511872, 3512808, 3551112, 3587409, 3628233, 3798613, 3813992, 4033503, 4104000, 4110848, 4123000, 4174281, 4206592, 4342914, 4467528, 4505949, 4511808, 4607064, 4624776, 4673088, 4744376, 4914000, 4931101, 5004125, 5135104, 5287707, 5318677, 5446359, 5462424, 5472152, 5639816, 5772403, 5799339, 5832729, 5835375, 6013000, 6017193, 6058747, 6230504, 6434883, 6445504, 6517000, 6742008, 7081984, 7091712, 7094269, 7365384, 7620661, 7640128, 7872536, 7882245, 7957504, 8029000, 8077888, 8131968, 8216000, 8275176, 8491392, 8493039, 8494577, 8587000, 8600256, 8647128, 8741824, 8849601, 8872487, 9016488, 9261729, 9443761, 9560896, 10036845, 10083528, 10202696, 10424232, 10469816, 10589696, 10648512, 10702783, 10765603, 10811017, 10821896, 10870119, 10962432, 11097567, 11261376, 11478584, 11548089, 11557000, 11855727, 11859211, 11985003, 12266856, 12533824, 12650337, 12753160, 12874176, 13484016, 13489875, 13490533, 13623913, 13731319, 13825728, 13832000, 13851000, 13874112, 13915125, 14197248, 14482503, 14765192, 14916727, 14978061, 15077907, 15187041, 15201368, 15398936, 15438250, 15682680, 16012269, 16387128, 16387189, 16587207, 16776487, 16797375, 16809984, 16983854, 17045567, 17999072, 18406603, 18410392, 18468513, 18617625, 18673625, 19034379, 19250163, 19346168, 20072017, 20127744, 20162952, 20496896, 20616463, 20683000, 20976832, 21036743, 21125384, 21411000, 21531608, 21753576, 21994875, 22031576, 22426369, 22543417, 22544704, 22754277, 22914304, 23901696, 23934528, 24480125, 24666560, 24767171, 24858171, 24897817, 25164405, 25371171, 25766208, 25785432, 25937576, 26122131, 26506467, 26569809, 26856576, 27000008, 27000064, 27003375, 27015625, 27262872, 27445392, 27529073, 27831951, 27882127, 28094976, 28102464, 28149336, 28408896, 28658448, 28699272, 28703269, 28981125, 29025864, 29184057, 29503656, 29791125, 30388904, 30511936, 31256000, 32114143, 32268024, 32530680, 32832000, 32886784, 32973759, 32984000, 33108264, 33394248, 33652736, 34031907, 34743312, 35740224, 35938728, 36047592, 36050904, 36094464, 36856512, 36998208, 37384704, 37498032, 37955008, 38007144, 38253878, 39312000, 39448808, 39639691, 40033000, 40134584, 40183262, 40354119, 40519115, 40970375, 41080832, 41258737, 41301953, 41343640, 41400639, 41436873, 41511232, 41892515, 42154840, 42168581, 42276843, 42301656, 42549416, 43450344, 43570872, 43699392, 43777216, 43852536, 43946000, 43997625, 44409995, 45118528, 45440551, 45882739, 46091997, 46179224, 46343059, 46394712, 46661832, 46683000, 46825128, 47915712, 48104000, 48137544, 48316662, 48469976, 49832523, 49844032, 49849856, 49933368, 50324625, 51240427, 51278929, 51479064, 51508639, 51564032, 52136000, 52242463, 52324272, 52739288, 53226297, 53283923, 53936064, 54267003, 54269091, 54814509, 54887625, 55306557, 55486125, 56388339, 56655872, 56733696, 56754152, 57066633, 58438072, 58751784, 58923072, 59913728, 60271939, 60698521, 60965288, 61121024, 61555832, 61568208, 62108397, 62135073, 62980288, 63057960, 63660032, 64125000, 64232000, 64421875, 64623104, 65055744, 65272753, 65293317, 65573928, 65728000, 66201408, 66469429, 66763333, 67173463, 67931136, 67944312, 67956616, 68007673, 68696000, 68802048, 69177024, 69583995, 69625969, 69805125, 69934592, 70449093, 70796808, 70957971, 70979896, 71292312, 71509312, 72131904, 72669177, 73369088, 73819863, 73842713, 74093832, 74097261, 74130875, 75550088, 76487168, 77129864, 77335776, 77414967, 79598125, 79692193, 80102574, 80208576, 80294760, 80668224, 80779032, 81621568, 83393856, 83758528, 84266000, 84637287, 84717568, 85188096, 85492792, 85502375, 85622264, 86124824, 86316741, 86368464, 86488136, 86575168, 86960952, 87029432, 87483968, 87539319, 87579037, 87699456, 87952501, 88122125, 88129323, 88780536, 89576767, 90091008, 90527229, 91034307, 91125027, 91125216, 91140435, 91828672, 92384712, 92456000, 94100426, 94820544, 94845816, 94873688, 95547816, 95731489, 95880024, 96753187, 96860043, 97867441, 97962291, 98040969, 98134848, 99768753, 100092456, 100270592, 100711000, 101194704, 101202696, 101615579, 101700872, 102025280, 102562551, 102977784, 102993408, 104212017, 105343875, 105997327, 106243219, 106496767, 107872128, 107919000, 107924264, 108904581, 108991304, 109850552, 110087432, 110605824, 110656000, 110808000, 110992896, 111321000, 111485673, 111906333, 112422709, 112705587, 113577984, 114103808, 115084125, 115860024, 115942104, 116215603, 116773741, 117132750, 117258678, 118121536, 118129375, 118974960, 119082880, 119164409, 119333816, 119377000, 119793457, 119824488, 120623256, 121287376, 121496328, 121610944, 121660623, 121818816, 122262264, 122810129, 123008375, 123191488, 123262120, 123506000, 124336000, 124390728, 124868952, 125461440, 126173376, 126217000, 126516061, 126906624, 127062000, 127396178, 127525671, 128098152, 128966383, 129333078, 129380329, 131097024, 131097512, 131126303, 131997229, 132678000, 132697656, 133139727, 134171875, 134211896, 134379000, 134479872, 135111375, 135870832, 136004184, 136364536, 136591000, 137467603, 137854899, 138090771, 138647808, 141117704, 141864697, 142098327, 142244648, 142768089, 143604279, 143992576, 144370863, 144404416, 145461771, 145908847, 146548376, 147051693, 147187369, 147252824, 147283136, 147485448, 147748104.

Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 870850 values, from 1729 to 999999259966294).

n\r 0  1 
2558502312348 2 
3489438196536184876 3 
453273215652125770155827 4 
5208643165249165548165897165513 5 
63125677951112891017687111702555966 6 
7552468428621163570011597443189 7 
852261378786128777783210119777351289377995 8 
948943816623527944000030301156932 9 
101316715861610642258599106478769721066335912610729859035 10 
117876779166792007927479333791877904379172792477915879303

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.