+-----+-- n=A084888(k) --+-----------------------------------------------------+ | k | n | A084889(n) | n^3 = u^2 + v^2 | +-----+-----+------------+-----------------------------------------------------+ | 1 | 2 | 1 | 8 = 4 + 4 = 2^2 + 2^2 | | 2 | 5 | 2 | 125 = 121 + 4 = 11^2 + 2^2 | | | | | = 100 + 25 = 10^2 + 5^2 | | 3 | 8 | 1 | 512 = 256 + 256 = 16^2 + 16^2 | | 4 | 10 | 2 | 1000 = 900 + 100 = 30^2 + 10^2 | | | | | = 676 + 324 = 26^2 + 18^2 | | 5 | 13 | 2 | 2197 = 2116 + 81 = 46^2 + 9^2 | | | | | = 1521 + 676 = 39^2 + 26^2 | | 6 | 17 | 2 | 4913 = 4624 + 289 = 68^2 + 17^2 | | | | | = 2704 + 2209 = 52^2 + 47^2 | | 7 | 18 | 1 | 5832 = 2916 + 2916 = 54^2 + 54^2 | | 8 | 20 | 2 | 8000 = 7744 + 256 = 88^2 + 16^2 | | | | | = 6400 + 1600 = 80^2 + 40^2 | | 9 | 25 | 3 | 15625 = 14400 + 1225 = 120^2 + 35^2 | | | | | = 13689 + 1936 = 117^2 + 44^2 | | | | | = 10000 + 5625 = 100^2 + 75^2 | | 10 | 26 | 2 | 17576 = 16900 + 676 = 130^2 + 26^2 | | | | | = 12100 + 5476 = 110^2 + 74^2 | | 11 | 29 | 2 | 24389 = 21025 + 3364 = 145^2 + 58^2 | | | | | = 20164 + 4225 = 142^2 + 65^2 | | 12 | 32 | 1 | 32768 = 16384 + 16384 = 128^2 + 128^2 | | 13 | 34 | 2 | 39304 = 39204 + 100 = 198^2 + 10^2 | | | | | = 28900 + 10404 = 170^2 + 102^2 | | 14 | 37 | 2 | 50653 = 49284 + 1369 = 222^2 + 37^2 | | | | | = 39204 + 11449 = 198^2 + 107^2 | | 15 | 40 | 2 | 64000 = 57600 + 6400 = 240^2 + 80^2 | | | | | = 43264 + 20736 = 208^2 + 144^2 | | 16 | 41 | 2 | 68921 = 55696 + 13225 = 236^2 + 115^2 | | | | | = 42025 + 26896 = 205^2 + 164^2 | | 17 | 45 | 2 | 91125 = 88209 + 2916 = 297^2 + 54^2 | | | | | = 72900 + 18225 = 270^2 + 135^2 | | 18 | 50 | 4 | 125000 = 122500 + 2500 = 350^2 + 50^2 | | | | | = 103684 + 21316 = 322^2 + 146^2 | | | | | = 96100 + 28900 = 310^2 + 170^2 | | | | | = 62500 + 62500 = 250^2 + 250^2 | | 19 | 52 | 2 | 140608 = 135424 + 5184 = 368^2 + 72^2 | | | | | = 97344 + 43264 = 312^2 + 208^2 | | 20 | 53 | 2 | 148877 = 137641 + 11236 = 371^2 + 106^2 | | | | | = 81796 + 67081 = 286^2 + 259^2 | | 21 | 58 | 2 | 195112 = 171396 + 23716 = 414^2 + 154^2 | | | | | = 164836 + 30276 = 406^2 + 174^2 | | 22 | 61 | 2 | 226981 = 172225 + 54756 = 415^2 + 234^2 | | | | | = 133956 + 93025 = 366^2 + 305^2 | | 23 | 65 | 8 | 274625 = 274576 + 49 = 524^2 + 7^2 | | | | | = 270400 + 4225 = 520^2 + 65^2 | | | | | = 255025 + 19600 = 505^2 + 140^2 | | | | | = 238144 + 36481 = 488^2 + 191^2 | | | | | = 231361 + 43264 = 481^2 + 208^2 | | | | | = 207025 + 67600 = 455^2 + 260^2 | | | | | = 172225 + 102400 = 415^2 + 320^2 | | | | | = 142129 + 132496 = 377^2 + 364^2 | | 24 | 68 | 2 | 314432 = 295936 + 18496 = 544^2 + 136^2 | Page 1+ +-----+-- n=A084888(k) --+-----------------------------------------------------+ | k | n | A084889(n) | n^3 = u^2 + v^2 | +-----+-----+------------+-----------------------------------------------------+ | | | | = 173056 + 141376 = 416^2 + 376^2 | | 25 | 72 | 1 | 373248 = 186624 + 186624 = 432^2 + 432^2 | | 26 | 73 | 2 | 389017 = 341056 + 47961 = 584^2 + 219^2 | | | | | = 301401 + 87616 = 549^2 + 296^2 | | 27 | 74 | 2 | 405224 = 372100 + 33124 = 610^2 + 182^2 | | | | | = 268324 + 136900 = 518^2 + 370^2 | | 28 | 80 | 2 | 512000 = 495616 + 16384 = 704^2 + 128^2 | | | | | = 409600 + 102400 = 640^2 + 320^2 | | 29 | 82 | 2 | 551368 = 544644 + 6724 = 738^2 + 82^2 | | | | | = 492804 + 58564 = 702^2 + 242^2 | | 30 | 85 | 8 | 614125 = 611524 + 2601 = 782^2 + 51^2 | | | | | = 585225 + 28900 = 765^2 + 170^2 | | | | | = 570025 + 44100 = 755^2 + 210^2 | | | | | = 532900 + 81225 = 730^2 + 285^2 | | | | | = 509796 + 104329 = 714^2 + 323^2 | | | | | = 443556 + 170569 = 666^2 + 413^2 | | | | | = 385641 + 228484 = 621^2 + 478^2 | | | | | = 354025 + 260100 = 595^2 + 510^2 | | 31 | 89 | 2 | 704969 = 697225 + 7744 = 835^2 + 88^2 | | | | | = 506944 + 198025 = 712^2 + 445^2 | | 32 | 90 | 2 | 729000 = 656100 + 72900 = 810^2 + 270^2 | | | | | = 492804 + 236196 = 702^2 + 486^2 | | 33 | 97 | 2 | 912673 = 824464 + 88209 = 908^2 + 297^2 | | | | | = 762129 + 150544 = 873^2 + 388^2 | | 34 | 98 | 1 | 941192 = 470596 + 470596 = 686^2 + 686^2 | | 35 | 100 | 3 | 1000000 = 921600 + 78400 = 960^2 + 280^2 | | | | | = 876096 + 123904 = 936^2 + 352^2 | | | | | = 640000 + 360000 = 800^2 + 600^2 | | 36 | 101 | 2 | 1030301 = 1020100 + 10201 = 1010^2 + 101^2 | | | | | = 940900 + 89401 = 970^2 + 299^2 | | 37 | 104 | 2 | 1124864 = 1081600 + 43264 = 1040^2 + 208^2 | | | | | = 774400 + 350464 = 880^2 + 592^2 | | 38 | 106 | 2 | 1191016 = 1188100 + 2916 = 1090^2 + 54^2 | | | | | = 910116 + 280900 = 954^2 + 530^2 | | 39 | 109 | 2 | 1295029 = 1188100 + 106929 = 1090^2 + 327^2 | | | | | = 762129 + 532900 = 873^2 + 730^2 | | 40 | 113 | 2 | 1442897 = 1002001 + 440896 = 1001^2 + 664^2 | | | | | = 817216 + 625681 = 904^2 + 791^2 | | 41 | 116 | 2 | 1560896 = 1345600 + 215296 = 1160^2 + 464^2 | | | | | = 1290496 + 270400 = 1136^2 + 520^2 | | 42 | 117 | 2 | 1601613 = 1542564 + 59049 = 1242^2 + 243^2 | | | | | = 1108809 + 492804 = 1053^2 + 702^2 | | 43 | 122 | 2 | 1815848 = 1800964 + 14884 = 1342^2 + 122^2 | | | | | = 1684804 + 131044 = 1298^2 + 362^2 | | 44 | 125 | 5 | 1953125 = 1932100 + 21025 = 1390^2 + 145^2 | | | | | = 1890625 + 62500 = 1375^2 + 250^2 | | | | | = 1562500 + 390625 = 1250^2 + 625^2 | | | | | = 1437601 + 515524 = 1199^2 + 718^2 | | | | | = 1050625 + 902500 = 1025^2 + 950^2 | | 45 | 128 | 1 | 2097152 = 1048576 + 1048576 = 1024^2 + 1024^2 | | 46 | 130 | 8 | 2197000 = 2196324 + 676 = 1482^2 + 26^2 | | | | | = 2160900 + 36100 = 1470^2 + 190^2 | Page 2+ +-----+-- n=A084888(k) --+-----------------------------------------------------+ | k | n | A084889(n) | n^3 = u^2 + v^2 | +-----+-----+------------+-----------------------------------------------------+ | | | | = 2044900 + 152100 = 1430^2 + 390^2 | | | | | = 1898884 + 298116 = 1378^2 + 546^2 | | | | | = 1844164 + 352836 = 1358^2 + 594^2 | | | | | = 1664100 + 532900 = 1290^2 + 730^2 | | | | | = 1368900 + 828100 = 1170^2 + 910^2 | | | | | = 1127844 + 1069156 = 1062^2 + 1034^2 | | 47 | 136 | 2 | 2515456 = 2509056 + 6400 = 1584^2 + 80^2 | | | | | = 1849600 + 665856 = 1360^2 + 816^2 | | 48 | 137 | 2 | 2571353 = 2271049 + 300304 = 1507^2 + 548^2 | | | | | = 1926544 + 644809 = 1388^2 + 803^2 | | 49 | 145 | 8 | 3048625 = 3045025 + 3600 = 1745^2 + 60^2 | | | | | = 3027600 + 21025 = 1740^2 + 145^2 | | | | | = 2927521 + 121104 = 1711^2 + 348^2 | | | | | = 2862864 + 185761 = 1692^2 + 431^2 | | | | | = 2187441 + 861184 = 1479^2 + 928^2 | | | | | = 2050624 + 998001 = 1432^2 + 999^2 | | | | | = 1849600 + 1199025 = 1360^2 + 1095^2 | | | | | = 1703025 + 1345600 = 1305^2 + 1160^2 | | 50 | 146 | 2 | 3112136 = 2856100 + 256036 = 1690^2 + 506^2 | | | | | = 2579236 + 532900 = 1606^2 + 730^2 | | 51 | 148 | 2 | 3241792 = 3154176 + 87616 = 1776^2 + 296^2 | | | | | = 2509056 + 732736 = 1584^2 + 856^2 | | 52 | 149 | 2 | 3307949 = 3087049 + 220900 = 1757^2 + 470^2 | | | | | = 2220100 + 1087849 = 1490^2 + 1043^2 | | 53 | 153 | 2 | 3581577 = 3370896 + 210681 = 1836^2 + 459^2 | | | | | = 1971216 + 1610361 = 1404^2 + 1269^2 | | 54 | 157 | 2 | 3869893 = 3849444 + 20449 = 1962^2 + 143^2 | | | | | = 2982529 + 887364 = 1727^2 + 942^2 | | 55 | 160 | 2 | 4096000 = 3686400 + 409600 = 1920^2 + 640^2 | | | | | = 2768896 + 1327104 = 1664^2 + 1152^2 | | 56 | 162 | 1 | 4251528 = 2125764 + 2125764 = 1458^2 + 1458^2 | | 57 | 164 | 2 | 4410944 = 3564544 + 846400 = 1888^2 + 920^2 | | | | | = 2689600 + 1721344 = 1640^2 + 1312^2 | | 58 | 169 | 3 | 4826809 = 4141225 + 685584 = 2035^2 + 828^2 | | | | | = 4112784 + 714025 = 2028^2 + 845^2 | | | | | = 2433600 + 2393209 = 1560^2 + 1547^2 | | 59 | 170 | 8 | 4913000 = 4884100 + 28900 = 2210^2 + 170^2 | | | | | = 4831204 + 81796 = 2198^2 + 286^2 | | | | | = 4656964 + 256036 = 2158^2 + 506^2 | | | | | = 4301476 + 611524 = 2074^2 + 782^2 | | | | | = 4120900 + 792100 = 2030^2 + 890^2 | | | | | = 3724900 + 1188100 = 1930^2 + 1090^2 | | | | | = 3496900 + 1416100 = 1870^2 + 1190^2 | | | | | = 2775556 + 2137444 = 1666^2 + 1462^2 | | 60 | 173 | 2 | 5177717 = 5058001 + 119716 = 2249^2 + 346^2 | | | | | = 4165681 + 1012036 = 2041^2 + 1006^2 | | 61 | 178 | 2 | 5639752 = 5354596 + 285156 = 2314^2 + 534^2 | | | | | = 3407716 + 2232036 = 1846^2 + 1494^2 | | 62 | 180 | 2 | 5832000 = 5645376 + 186624 = 2376^2 + 432^2 | | | | | = 4665600 + 1166400 = 2160^2 + 1080^2 | | 63 | 181 | 2 | 5929741 = 3884841 + 2044900 = 1971^2 + 1430^2 | | | | | = 3276100 + 2653641 = 1810^2 + 1629^2 | Page 3+ +-----+-- n=A084888(k) --+-----------------------------------------------------+ | k | n | A084889(n) | n^3 = u^2 + v^2 | +-----+-----+------------+-----------------------------------------------------+ | 64 | 185 | 8 | 6331625 = 6330256 + 1369 = 2516^2 + 37^2 | | | | | = 6325225 + 6400 = 2515^2 + 80^2 | | | | | = 5784025 + 547600 = 2405^2 + 740^2 | | | | | = 5721664 + 609961 = 2392^2 + 781^2 | | | | | = 5607424 + 724201 = 2368^2 + 851^2 | | | | | = 4243600 + 2088025 = 2060^2 + 1445^2 | | | | | = 4141225 + 2190400 = 2035^2 + 1480^2 | | | | | = 3857296 + 2474329 = 1964^2 + 1573^2 | | 65 | 193 | 2 | 7189057 = 7187761 + 1296 = 2681^2 + 36^2 | | | | | = 5363856 + 1825201 = 2316^2 + 1351^2 | | 66 | 194 | 2 | 7301384 = 6360484 + 940900 = 2522^2 + 970^2 | | | | | = 5808100 + 1493284 = 2410^2 + 1222^2 | | 67 | 197 | 2 | 7645373 = 7606564 + 38809 = 2758^2 + 197^2 | | | | | = 7300804 + 344569 = 2702^2 + 587^2 | | 68 | 200 | 4 | 8000000 = 7840000 + 160000 = 2800^2 + 400^2 | | | | | = 6635776 + 1364224 = 2576^2 + 1168^2 | | | | | = 6150400 + 1849600 = 2480^2 + 1360^2 | | | | | = 4000000 + 4000000 = 2000^2 + 2000^2 | | 69 | 202 | 2 | 8242408 = 6441444 + 1800964 = 2538^2 + 1342^2 | | | | | = 4937284 + 3305124 = 2222^2 + 1818^2 | | 70 | 205 | 8 | 8615125 = 8614225 + 900 = 2935^2 + 30^2 | | | | | = 8236900 + 378225 = 2870^2 + 615^2 | | | | | = 7986276 + 628849 = 2826^2 + 793^2 | | | | | = 7102225 + 1512900 = 2665^2 + 1230^2 | | | | | = 6671889 + 1943236 = 2583^2 + 1394^2 | | | | | = 5597956 + 3017169 = 2366^2 + 1737^2 | | | | | = 5428900 + 3186225 = 2330^2 + 1785^2 | | | | | = 4901796 + 3713329 = 2214^2 + 1927^2 | | 71 | 208 | 2 | 8998912 = 8667136 + 331776 = 2944^2 + 576^2 | | | | | = 6230016 + 2768896 = 2496^2 + 1664^2 | | 72 | 212 | 2 | 9528128 = 8809024 + 719104 = 2968^2 + 848^2 | | | | | = 5234944 + 4293184 = 2288^2 + 2072^2 | | 73 | 218 | 2 | 10360232 = 10278436 + 81796 = 3206^2 + 286^2 | | | | | = 8031556 + 2328676 = 2834^2 + 1526^2 | | 74 | 221 | 8 | 10793861 = 10764961 + 28900 = 3281^2 + 170^2 | | | | | = 10562500 + 231361 = 3250^2 + 481^2 | | | | | = 10144225 + 649636 = 3185^2 + 806^2 | | | | | = 9572836 + 1221025 = 3094^2 + 1105^2 | | | | | = 8850625 + 1943236 = 2975^2 + 1394^2 | | | | | = 7924225 + 2869636 = 2815^2 + 1694^2 | | | | | = 6916900 + 3876961 = 2630^2 + 1969^2 | | | | | = 5909761 + 4884100 = 2431^2 + 2210^2 | | 75 | 225 | 3 | 11390625 = 10497600 + 893025 = 3240^2 + 945^2 | | | | | = 9979281 + 1411344 = 3159^2 + 1188^2 | | | | | = 7290000 + 4100625 = 2700^2 + 2025^2 | | 76 | 226 | 2 | 11543176 = 11492100 + 51076 = 3390^2 + 226^2 | | | | | = 11088900 + 454276 = 3330^2 + 674^2 | | 77 | 229 | 2 | 12008989 = 11799225 + 209764 = 3435^2 + 458^2 | | | | | = 10208025 + 1800964 = 3195^2 + 1342^2 | | 78 | 232 | 2 | 12487168 = 10969344 + 1517824 = 3312^2 + 1232^2 | | | | | = 10549504 + 1937664 = 3248^2 + 1392^2 | | 79 | 233 | 2 | 12649337 = 12559936 + 89401 = 3544^2 + 299^2 | Page 4+ +-----+-- n=A084888(k) --+-----------------------------------------------------+ | k | n | A084889(n) | n^3 = u^2 + v^2 | +-----+-----+------------+-----------------------------------------------------+ | | | | = 9174841 + 3474496 = 3029^2 + 1864^2 | | 80 | 234 | 2 | 12812904 = 12320100 + 492804 = 3510^2 + 702^2 | | | | | = 8820900 + 3992004 = 2970^2 + 1998^2 | | 81 | 241 | 2 | 13997521 = 13068225 + 929296 = 3615^2 + 964^2 | | | | | = 7049025 + 6948496 = 2655^2 + 2636^2 | | 82 | 242 | 1 | 14172488 = 7086244 + 7086244 = 2662^2 + 2662^2 | | 83 | 244 | 2 | 14526784 = 11022400 + 3504384 = 3320^2 + 1872^2 | | | | | = 8573184 + 5953600 = 2928^2 + 2440^2 | | 84 | 245 | 2 | 14706125 = 14235529 + 470596 = 3773^2 + 686^2 | | | | | = 11764900 + 2941225 = 3430^2 + 1715^2 | | 85 | 250 | 5 | 15625000 = 15602500 + 22500 = 3950^2 + 150^2 | | | | | = 14699556 + 925444 = 3834^2 + 962^2 | | | | | = 14062500 + 1562500 = 3750^2 + 1250^2 | | | | | = 10562500 + 5062500 = 3250^2 + 2250^2 | | | | | = 9424900 + 6200100 = 3070^2 + 2490^2 | | 86 | 257 | 2 | 16974593 = 16908544 + 66049 = 4112^2 + 257^2 | | | | | = 16386304 + 588289 = 4048^2 + 767^2 | | 87 | 260 | 8 | 17576000 = 17572864 + 3136 = 4192^2 + 56^2 | | | | | = 17305600 + 270400 = 4160^2 + 520^2 | | | | | = 16321600 + 1254400 = 4040^2 + 1120^2 | | | | | = 15241216 + 2334784 = 3904^2 + 1528^2 | | | | | = 14807104 + 2768896 = 3848^2 + 1664^2 | | | | | = 13249600 + 4326400 = 3640^2 + 2080^2 | | | | | = 11022400 + 6553600 = 3320^2 + 2560^2 | | | | | = 9096256 + 8479744 = 3016^2 + 2912^2 | | 88 | 261 | 2 | 17779581 = 15327225 + 2452356 = 3915^2 + 1566^2 | | | | | = 14699556 + 3080025 = 3834^2 + 1755^2 | | 89 | 265 | 8 | 18609625 = 18429849 + 179776 = 4293^2 + 424^2 | | | | | = 17977600 + 632025 = 4240^2 + 795^2 | | | | | = 17264025 + 1345600 = 4155^2 + 1160^2 | | | | | = 16160400 + 2449225 = 4020^2 + 1565^2 | | | | | = 14969161 + 3640464 = 3869^2 + 1908^2 | | | | | = 13424896 + 5184729 = 3664^2 + 2277^2 | | | | | = 11703241 + 6906384 = 3421^2 + 2628^2 | | | | | = 10112400 + 8497225 = 3180^2 + 2915^2 | | 90 | 269 | 2 | 19465109 = 16564900 + 2900209 = 4070^2 + 1703^2 | | | | | = 12229009 + 7236100 = 3497^2 + 2690^2 | | 91 | 272 | 2 | 20123648 = 18939904 + 1183744 = 4352^2 + 1088^2 | | | | | = 11075584 + 9048064 = 3328^2 + 3008^2 | | 92 | 274 | 2 | 20570824 = 19201924 + 1368900 = 4382^2 + 1170^2 | | | | | = 16892100 + 3678724 = 4110^2 + 1918^2 | | 93 | 277 | 2 | 21253933 = 20820969 + 432964 = 4563^2 + 658^2 | | | | | = 15038884 + 6215049 = 3878^2 + 2493^2 | | 94 | 281 | 2 | 22188041 = 20214016 + 1974025 = 4496^2 + 1405^2 | | | | | = 13801225 + 8386816 = 3715^2 + 2896^2 | | 95 | 288 | 1 | 23887872 = 11943936 + 11943936 = 3456^2 + 3456^2 | | 96 | 289 | 3 | 24137569 = 23892544 + 245025 = 4888^2 + 495^2 | | | | | = 18792225 + 5345344 = 4335^2 + 2312^2 | | | | | = 16646400 + 7491169 = 4080^2 + 2737^2 | | 97 | 290 | 8 | 24389000 = 24304900 + 84100 = 4930^2 + 290^2 | | | | | = 24108100 + 280900 = 4910^2 + 530^2 | | | | | = 23639044 + 749956 = 4862^2 + 866^2 | Page 5+ +-----+-- n=A084888(k) --+-----------------------------------------------------+ | k | n | A084889(n) | n^3 = u^2 + v^2 | +-----+-----+------------+-----------------------------------------------------+ | | | | = 23174596 + 1214404 = 4814^2 + 1102^2 | | | | | = 18028516 + 6360484 = 4246^2 + 2522^2 | | | | | = 16957924 + 7431076 = 4118^2 + 2726^2 | | | | | = 14212900 + 10176100 = 3770^2 + 3190^2 | | | | | = 13032100 + 11356900 = 3610^2 + 3370^2 | | 98 | 292 | 2 | 24897088 = 21827584 + 3069504 = 4672^2 + 1752^2 | | | | | = 19289664 + 5607424 = 4392^2 + 2368^2 | | 99 | 293 | 2 | 25153757 = 24810361 + 343396 = 4981^2 + 586^2 | | | | | = 22174681 + 2979076 = 4709^2 + 1726^2 | | 100 | 296 | 2 | 25934336 = 23814400 + 2119936 = 4880^2 + 1456^2 | | | | | = 17172736 + 8761600 = 4144^2 + 2960^2 | | 101 | 298 | 2 | 26463592 = 25664356 + 799236 = 5066^2 + 894^2 | | | | | = 19838116 + 6625476 = 4454^2 + 2574^2 | | 102 | 305 | 8 | 28372625 = 28302400 + 70225 = 5320^2 + 265^2 | | | | | = 26884225 + 1488400 = 5185^2 + 1220^2 | | | | | = 25331089 + 3041536 = 5033^2 + 1744^2 | | | | | = 23814400 + 4558225 = 4880^2 + 2135^2 | | | | | = 21492496 + 6880129 = 4636^2 + 2623^2 | | | | | = 19492225 + 8880400 = 4415^2 + 2980^2 | | | | | = 16785409 + 11587216 = 4097^2 + 3404^2 | | | | | = 16703569 + 11669056 = 4087^2 + 3416^2 | | 103 | 306 | 2 | 28652616 = 28579716 + 72900 = 5346^2 + 270^2 | | | | | = 21068100 + 7584516 = 4590^2 + 2754^2 | | 104 | 313 | 2 | 30664297 = 18974736 + 11689561 = 4356^2 + 3419^2 | | | | | = 16556761 + 14107536 = 4069^2 + 3756^2 | | 105 | 314 | 2 | 30959144 = 28494244 + 2464900 = 5338^2 + 1570^2 | | | | | = 17724100 + 13235044 = 4210^2 + 3638^2 | | 106 | 317 | 2 | 31855013 = 26388769 + 5466244 = 5137^2 + 2338^2 | | | | | = 19695844 + 12159169 = 4438^2 + 3487^2 | | 107 | 320 | 2 | 32768000 = 31719424 + 1048576 = 5632^2 + 1024^2 | | | | | = 26214400 + 6553600 = 5120^2 + 2560^2 | | 108 | 325 | 14 | 34328125 = 34222500 + 105625 = 5850^2 + 325^2 | | | | | = 34047225 + 280900 = 5835^2 + 530^2 | | | | | = 33385284 + 942841 = 5778^2 + 971^2 | | | | | = 33062500 + 1265625 = 5750^2 + 1125^2 | | | | | = 32569849 + 1758276 = 5707^2 + 1326^2 | | | | | = 31248100 + 3080025 = 5590^2 + 1755^2 | | | | | = 30525625 + 3802500 = 5525^2 + 1950^2 | | | | | = 27825625 + 6502500 = 5275^2 + 2550^2 | | | | | = 27092025 + 7236100 = 5205^2 + 2690^2 | | | | | = 24860196 + 9467929 = 4986^2 + 3077^2 | | | | | = 23765625 + 10562500 = 4875^2 + 3250^2 | | | | | = 22638564 + 11689561 = 4758^2 + 3419^2 | | | | | = 20115225 + 14212900 = 4485^2 + 3770^2 | | | | | = 18922500 + 15405625 = 4350^2 + 3925^2 | | 109 | 328 | 2 | 35287552 = 34857216 + 430336 = 5904^2 + 656^2 | | | | | = 31539456 + 3748096 = 5616^2 + 1936^2 | | 110 | 333 | 2 | 36926037 = 35928036 + 998001 = 5994^2 + 999^2 | | | | | = 28579716 + 8346321 = 5346^2 + 2889^2 | | 111 | 337 | 2 | 38272753 = 38229489 + 43264 = 6183^2 + 208^2 | | | | | = 29073664 + 9199089 = 5392^2 + 3033^2 | | 112 | 338 | 4 | 38614472 = 38613796 + 676 = 6214^2 + 26^2 | Page 6+ +-----+-- n=A084888(k) --+-----------------------------------------------------+ | k | n | A084889(n) | n^3 = u^2 + v^2 | +-----+-----+------------+-----------------------------------------------------+ | | | | = 33016516 + 5597956 = 5746^2 + 2366^2 | | | | | = 32787076 + 5827396 = 5726^2 + 2414^2 | | | | | = 19307236 + 19307236 = 4394^2 + 4394^2 | | 113 | 340 | 8 | 39304000 = 39137536 + 166464 = 6256^2 + 408^2 | | | | | = 37454400 + 1849600 = 6120^2 + 1360^2 | | | | | = 36481600 + 2822400 = 6040^2 + 1680^2 | | | | | = 34105600 + 5198400 = 5840^2 + 2280^2 | | | | | = 32626944 + 6677056 = 5712^2 + 2584^2 | | | | | = 28387584 + 10916416 = 5328^2 + 3304^2 | | | | | = 24681024 + 14622976 = 4968^2 + 3824^2 | | | | | = 22657600 + 16646400 = 4760^2 + 4080^2 | | 114 | 346 | 2 | 41421736 = 37136836 + 4284900 = 6094^2 + 2070^2 | | | | | = 26936100 + 14485636 = 5190^2 + 3806^2 | | 115 | 349 | 2 | 42508549 = 39463524 + 3045025 = 6282^2 + 1745^2 | | | | | = 22420225 + 20088324 = 4735^2 + 4482^2 | | 116 | 353 | 2 | 43986977 = 41267776 + 2719201 = 6424^2 + 1649^2 | | | | | = 36012001 + 7974976 = 6001^2 + 2824^2 | | 117 | 356 | 2 | 45118016 = 44622400 + 495616 = 6680^2 + 704^2 | | | | | = 32444416 + 12673600 = 5696^2 + 3560^2 | | 118 | 360 | 2 | 46656000 = 41990400 + 4665600 = 6480^2 + 2160^2 | | | | | = 31539456 + 15116544 = 5616^2 + 3888^2 | | 119 | 362 | 2 | 47437928 = 47306884 + 131044 = 6878^2 + 362^2 | | | | | = 46267204 + 1170724 = 6802^2 + 1082^2 | | 120 | 365 | 8 | 48627125 = 48580900 + 46225 = 6970^2 + 215^2 | | | | | = 48094225 + 532900 = 6935^2 + 730^2 | | | | | = 47087044 + 1540081 = 6862^2 + 1241^2 | | | | | = 43970161 + 4656964 = 6631^2 + 2158^2 | | | | | = 35832196 + 12794929 = 5986^2 + 3577^2 | | | | | = 32547025 + 16080100 = 5705^2 + 4010^2 | | | | | = 29669809 + 18957316 = 5447^2 + 4354^2 | | | | | = 26112100 + 22515025 = 5110^2 + 4745^2 | | 121 | 369 | 2 | 50243409 = 40602384 + 9641025 = 6372^2 + 3105^2 | | | | | = 30636225 + 19607184 = 5535^2 + 4428^2 | | 122 | 370 | 8 | 50653000 = 50041476 + 611524 = 7074^2 + 782^2 | | | | | = 49420900 + 1232100 = 7030^2 + 1110^2 | | | | | = 49140100 + 1512900 = 7010^2 + 1230^2 | | | | | = 41447844 + 9205156 = 6438^2 + 3034^2 | | | | | = 40271716 + 10381284 = 6346^2 + 3222^2 | | | | | = 39564100 + 11088900 = 6290^2 + 3330^2 | | | | | = 26936100 + 23716900 = 5190^2 + 4870^2 | | | | | = 26071236 + 24581764 = 5106^2 + 4958^2 | | 123 | 373 | 2 | 51895117 = 45077796 + 6817321 = 6714^2 + 2611^2 | | | | | = 41744521 + 10150596 = 6461^2 + 3186^2 | | 124 | 377 | 8 | 53582633 = 52243984 + 1338649 = 7228^2 + 1157^2 | | | | | = 51724864 + 1857769 = 7192^2 + 1363^2 | | | | | = 51308569 + 2274064 = 7163^2 + 1508^2 | | | | | = 50651689 + 2930944 = 7117^2 + 1712^2 | | | | | = 38775529 + 14807104 = 6227^2 + 3848^2 | | | | | = 37797904 + 15784729 = 6148^2 + 3973^2 | | | | | = 36385024 + 17197609 = 6032^2 + 4147^2 | | | | | = 35366809 + 18215824 = 5947^2 + 4268^2 | | 125 | 386 | 2 | 57512456 = 53787556 + 3724900 = 7334^2 + 1930^2 | Page 7+ +-----+-- n=A084888(k) --+-----------------------------------------------------+ | k | n | A084889(n) | n^3 = u^2 + v^2 | +-----+-----+------------+-----------------------------------------------------+ | | | | = 29528356 + 27984100 = 5434^2 + 5290^2 | | 126 | 388 | 2 | 58411072 = 52765696 + 5645376 = 7264^2 + 2376^2 | | | | | = 48776256 + 9634816 = 6984^2 + 3104^2 | | 127 | 389 | 2 | 58863869 = 58828900 + 34969 = 7670^2 + 187^2 | | | | | = 43731769 + 15132100 = 6613^2 + 3890^2 | | 128 | 392 | 1 | 60236288 = 30118144 + 30118144 = 5488^2 + 5488^2 | | 129 | 394 | 2 | 61162984 = 43270084 + 17892900 = 6578^2 + 4230^2 | | | | | = 34928100 + 26234884 = 5910^2 + 5122^2 | | 130 | 397 | 2 | 62570773 = 56896849 + 5673924 = 7543^2 + 2382^2 | | | | | = 39463524 + 23107249 = 6282^2 + 4807^2 | | 131 | 400 | 3 | 64000000 = 58982400 + 5017600 = 7680^2 + 2240^2 | | | | | = 56070144 + 7929856 = 7488^2 + 2816^2 | | | | | = 40960000 + 23040000 = 6400^2 + 4800^2 | | 132 | 401 | 2 | 64481201 = 64320400 + 160801 = 8020^2 + 401^2 | | | | | = 63043600 + 1437601 = 7940^2 + 1199^2 | | 133 | 404 | 2 | 65939264 = 65286400 + 652864 = 8080^2 + 808^2 | | | | | = 60217600 + 5721664 = 7760^2 + 2392^2 | | 134 | 405 | 2 | 66430125 = 64304361 + 2125764 = 8019^2 + 1458^2 | | | | | = 53144100 + 13286025 = 7290^2 + 3645^2 | | 135 | 409 | 2 | 68417929 = 66912400 + 1505529 = 8180^2 + 1227^2 | | | | | = 55651600 + 12766329 = 7460^2 + 3573^2 | | 136 | 410 | 8 | 68921000 = 68591524 + 329476 = 8282^2 + 574^2 | | | | | = 67732900 + 1188100 = 8230^2 + 1090^2 | | | | | = 67338436 + 1582564 = 8206^2 + 1258^2 | | | | | = 63266116 + 5654884 = 7954^2 + 2378^2 | | | | | = 60684100 + 8236900 = 7790^2 + 2870^2 | | | | | = 52388644 + 16532356 = 7238^2 + 4066^2 | | | | | = 48580900 + 20340100 = 6970^2 + 4510^2 | | | | | = 35164900 + 33756100 = 5930^2 + 5810^2 | | 137 | 416 | 2 | 71991296 = 69222400 + 2768896 = 8320^2 + 1664^2 | | | | | = 49561600 + 22429696 = 7040^2 + 4736^2 | | 138 | 421 | 2 | 74618461 = 44970436 + 29648025 = 6706^2 + 5445^2 | | | | | = 39879225 + 34739236 = 6315^2 + 5894^2 | | 139 | 424 | 2 | 76225024 = 76038400 + 186624 = 8720^2 + 432^2 | | | | | = 58247424 + 17977600 = 7632^2 + 4240^2 | | 140 | 425 | 14 | 76765625 = 76650025 + 115600 = 8755^2 + 340^2 | | | | | = 76125625 + 640000 = 8725^2 + 800^2 | | | | | = 75759616 + 1006009 = 8704^2 + 1003^2 | | | | | = 73960000 + 2805625 = 8600^2 + 1675^2 | | | | | = 72250000 + 4515625 = 8500^2 + 2125^2 | | | | | = 66455104 + 10310521 = 8152^2 + 3211^2 | | | | | = 65205625 + 11560000 = 8075^2 + 3400^2 | | | | | = 62173225 + 14592400 = 7885^2 + 3820^2 | | | | | = 60637369 + 16128256 = 7787^2 + 4016^2 | | | | | = 57229225 + 19536400 = 7565^2 + 4420^2 | | | | | = 55651600 + 21114025 = 7460^2 + 4595^2 | | | | | = 51955264 + 24810361 = 7208^2 + 4981^2 | | | | | = 46240000 + 30525625 = 6800^2 + 5525^2 | | | | | = 42250000 + 34515625 = 6500^2 + 5875^2 | | 141 | 433 | 2 | 81182737 = 75272976 + 5909761 = 8676^2 + 2431^2 | | | | | = 54184321 + 26998416 = 7361^2 + 5196^2 | | 142 | 436 | 2 | 82881856 = 76038400 + 6843456 = 8720^2 + 2616^2 | Page 8+ +-----+-- n=A084888(k) --+-----------------------------------------------------+ | k | n | A084889(n) | n^3 = u^2 + v^2 | +-----+-----+------------+-----------------------------------------------------+ | | | | = 48776256 + 34105600 = 6984^2 + 5840^2 | | 143 | 442 | 8 | 86350888 = 86155524 + 195364 = 9282^2 + 442^2 | | | | | = 84603204 + 1747684 = 9198^2 + 1322^2 | | | | | = 81324324 + 5026564 = 9018^2 + 2242^2 | | | | | = 76352644 + 9998244 = 8738^2 + 3162^2 | | | | | = 70526404 + 15824484 = 8398^2 + 3978^2 | | | | | = 63712324 + 22638564 = 7982^2 + 4758^2 | | | | | = 55681444 + 30669444 = 7462^2 + 5538^2 | | | | | = 47637604 + 38713284 = 6902^2 + 6222^2 | | 144 | 445 | 8 | 88121125 = 87628321 + 492804 = 9361^2 + 702^2 | | | | | = 87329025 + 792100 = 9345^2 + 890^2 | | | | | = 81162081 + 6959044 = 9009^2 + 2638^2 | | | | | = 77264100 + 10857025 = 8790^2 + 3295^2 | | | | | = 76073284 + 12047841 = 8722^2 + 3471^2 | | | | | = 64160100 + 23961025 = 8010^2 + 4895^2 | | | | | = 62568100 + 25553025 = 7910^2 + 5055^2 | | | | | = 48191364 + 39929761 = 6942^2 + 6319^2 | | 145 | 449 | 2 | 90518849 = 80640400 + 9878449 = 8980^2 + 3143^2 | | | | | = 64915249 + 25603600 = 8057^2 + 5060^2 | | 146 | 450 | 4 | 91125000 = 89302500 + 1822500 = 9450^2 + 1350^2 | | | | | = 75585636 + 15539364 = 8694^2 + 3942^2 | | | | | = 70056900 + 21068100 = 8370^2 + 4590^2 | | | | | = 45562500 + 45562500 = 6750^2 + 6750^2 | | 147 | 452 | 2 | 92345408 = 64128064 + 28217344 = 8008^2 + 5312^2 | | | | | = 52301824 + 40043584 = 7232^2 + 6328^2 | | 148 | 457 | 2 | 95443993 = 92102409 + 3341584 = 9597^2 + 1828^2 | | | | | = 68112009 + 27331984 = 8253^2 + 5228^2 | | 149 | 458 | 2 | 96071912 = 82337476 + 13734436 = 9074^2 + 3706^2 | | | | | = 60621796 + 35450116 = 7786^2 + 5954^2 | | 150 | 461 | 2 | 97972181 = 96628900 + 1343281 = 9830^2 + 1159^2 | | | | | = 76720081 + 21252100 = 8759^2 + 4610^2 | | 151 | 464 | 2 | 99897344 = 86118400 + 13778944 = 9280^2 + 3712^2 | | | | | = 82591744 + 17305600 = 9088^2 + 4160^2 | | 152 | 466 | 2 | 101194696 = 95765796 + 5428900 = 9786^2 + 2330^2 | | | | | = 59074596 + 42120100 = 7686^2 + 6490^2 | | 153 | 468 | 2 | 102503232 = 98724096 + 3779136 = 9936^2 + 1944^2 | | | | | = 70963776 + 31539456 = 8424^2 + 5616^2 | | 154 | 477 | 2 | 108531333 = 100340289 + 8191044 = 10017^2 + 2862^2 | | | | | = 59629284 + 48902049 = 7722^2 + 6993^2 | | 155 | 481 | 8 | 111284641 = 111197025 + 87616 = 10545^2 + 296^2 | | | | | = 110334016 + 950625 = 10504^2 + 975^2 | | | | | = 101425041 + 9859600 = 10071^2 + 3140^2 | | | | | = 97594641 + 13690000 = 9879^2 + 3700^2 | | | | | = 92544400 + 18740241 = 9620^2 + 4329^2 | | | | | = 86881041 + 24403600 = 9321^2 + 4940^2 | | | | | = 66341025 + 44943616 = 8145^2 + 6704^2 | | | | | = 59228416 + 52056225 = 7696^2 + 7215^2 | | 156 | 482 | 2 | 111980168 = 111978724 + 1444 = 10582^2 + 38^2 | | | | | = 83868964 + 28111204 = 9158^2 + 5302^2 | | 157 | 485 | 8 | 114084125 = 113848900 + 235225 = 10670^2 + 485^2 | | | | | = 111978724 + 2105401 = 10582^2 + 1451^2 | | | | | = 111619225 + 2464900 = 10565^2 + 1570^2 | Page 9+ +-----+-- n=A084888(k) --+-----------------------------------------------------+ | k | n | A084889(n) | n^3 = u^2 + v^2 | +-----+-----+------------+-----------------------------------------------------+ | | | | = 107723641 + 6360484 = 10379^2 + 2522^2 | | | | | = 88247236 + 25836889 = 9394^2 + 5083^2 | | | | | = 77915929 + 36168196 = 8827^2 + 6014^2 | | | | | = 67980025 + 46104100 = 8245^2 + 6790^2 | | | | | = 57684025 + 56400100 = 7595^2 + 7510^2 | | 158 | 488 | 2 | 116214272 = 115261696 + 952576 = 10736^2 + 976^2 | | | | | = 107827456 + 8386816 = 10384^2 + 2896^2 | | 159 | 490 | 2 | 117649000 = 105884100 + 11764900 = 10290^2 + 3430^2 | | | | | = 79530724 + 38118276 = 8918^2 + 6174^2 | | 160 | 493 | 8 | 119823157 = 117635716 + 2187441 = 10846^2 + 1479^2 | | | | | = 115799121 + 4024036 = 10761^2 + 2006^2 | | | | | = 108972721 + 10850436 = 10439^2 + 3294^2 | | | | | = 105390756 + 14432401 = 10266^2 + 3799^2 | | | | | = 101082916 + 18740241 = 10054^2 + 4329^2 | | | | | = 96648561 + 23174596 = 9831^2 + 4814^2 | | | | | = 78747876 + 41075281 = 8874^2 + 6409^2 | | | | | = 73119601 + 46703556 = 8551^2 + 6834^2 | | 161 | 500 | 5 | 125000000 = 123654400 + 1345600 = 11120^2 + 1160^2 | | | | | = 121000000 + 4000000 = 11000^2 + 2000^2 | | | | | = 100000000 + 25000000 = 10000^2 + 5000^2 | | | | | = 92006464 + 32993536 = 9592^2 + 5744^2 | | | | | = 67240000 + 57760000 = 8200^2 + 7600^2 | +-----+-----+------------+-----------------------------------------------------+ Page 10 Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Jun 10 2003