Nastenka / Message Board Pomoc / Help Virtual/Numbers Patterns 6.00000000 6 = 1! + 2! 6.00000000 6 = (1 + 2)! 6.00000000 6 = 1 + 2 + 3 6.00000000 6 = 1 * 2 * 3 _________________________________________________________________ 1.00000000 1 = 2^0 = 1^0 3.00000000 3 = 3 = 2 + 1 25.0000000 25 = 5^2 = 4^2 + 3^2 216.000000 ' 216 = 6^3 = 5^3 + 4^3 + 3^3 _________________________________________________________________ 841.000000 ' 841 = 29^2 = 20^2 + 21^2 4900.00000 ' 4900 = 70^2 = 1^2 + 2^2 + ... + 23^3 + 24^2 5929.00000 ' 5929 = 77^2 = 18^2 + 19^2 + ... + 27^3 + 28^2 8464.00000 ' 8464 = 92^2 = 7^2 + 8^2 + ... + 28^3 + 29^2 8000.00000 ' 8000 = 20^3 = 11^3 + 12^3 + 13^3 + 14^3 64000.0000 ' = 40^3 = 3^3 + 4^3 + ... + 21^3 + 22^3 216000.000 ' = 60^3 = 6^3 + 7^3 + ... + 29^3 + 30^3 343000.000 ' = 70^3 = 15^3 + 16^3 + ... + 33^3 + 34^3 5832000.00 ' = 180^3 = 6^3 + 7^3 + ... + 68^3 + 69^3 35937000.0 ' = 330^3 = 11^3 + 12^3 + ... + 108^3 + 109^3 157464000. ' = 540^3 = 34^3 + 35^3 + ... + 157^3 + 158^3 _________________________________________________________________ 81.0000000 81 = (8 + 1)^2 512.000000 512 = (5 + 1 + 2)^3 4913.00000 4913 = (4 + 9 + 1 + 3)^3 5832.00000 5832 = (5 + 8 + 3 + 2)^3 17576.0000 = (1 + 7 + 5 + 7 + 6)^3 19683.0000 = (1 + 9 + 6 + 8 + 3)^3 2401.00000 2401 = (2 + 4 + 0 + 1)^4 234256.000 = (2 + 3 + 4 + 2 + 5 + 6)^4 390625.000 = (3 + 9 + 0 + 6 + 2 + 5)^4 614656.000 = (6 + 1 + 4 + 6 + 5 + 6)^4 1679616.00 = (1 + 6 + 7 + ... + 1 + 6)^4 17210368.0 = (1 + 7 + 2 + ... + 6 + 8)^5 52521875.0 = (5 + 2 + 5 + ... + 7 + 5)^5 60466176.0 = (6 + 0 + 4 + ... + 7 + 6)^5 34012224.0 = (3 + 4 + 0 + ... + 2 + 4)^6 _________________________________________________________________ 89.0000000 89 = 8 + 9^2 135.000000 135 = 1 + 3^2 + 5^3 175.000000 175 = 1 + 7^2 + 5^3 518.000000 518 = 5 + 1^2 + 8^3 598.000000 598 = 5 + 9^2 + 8^3 1306.00000 ' 1306 = 1 + 3^2 + 0^3 + 6^4 1676.00000 ' 1676 = 1 + 6^2 + 7^3 + 6^4 2427.00000 ' 2427 = 2 + 4^2 + 2^3 + 7^4 153.000000 153 = 1^3 + 5^3 + 3^3 370.000000 370 = 3^3 + 7^3 + 0^3 371.000000 371 = 3^3 + 7^3 + 1^3 407.000000 407 = 4^3 + 0^3 + 7^3 1634.00000 1634 = 1^4 + 6^4 + 3^4 + 4^4 8208.00000 8208 = 8^4 + 2^4 + 0^4 + 8^4 9474.00000 ' 9474 = 9^4 + 4^4 + 7^4 + 4^4 4150.00000 ' 4150 = 4^5 + 1^5 + 5^5 + 0^5 4151.00000 ' 4151 = 4^5 + 1^5 + 5^5 + 1^5 54748.0000 ' = 5^5 + 4^5 + 7^5 + 4^5 + 8^5 92727.0000 ' = 9^5 + 2^5 + 7^5 + 2^5 + 7^5 93084.0000 ' = 9^5 + 3^5 + 0^5 + 8^5 + 4^5 194979.000 ' = 1^5 + 9^5 + 4^5 + 9^5 + 7^5 + 9^5 548834.000 ' = 5^6 + 4^6 + 8^6 + 8^6 + 3^6 + 4^6 1741725.00 ' = 1^7 + 7^7 + 4^7 + ... + 2^7 + 5^7 4210818.00 ' = 4^7 + 2^7 + 1^7 + ... + 1^7 + 8^7 9800817.00 ' = 9^7 + 8^7 + 0^7 + ... + 1^7 + 7^7 9926315.00 ' = 9^7 + 9^7 + 2^7 + ... + 1^7 + 5^7 14459929.0 ' = 1^7 + 4^7 + 4^7 + ... + 2^7 + 9^7 24678050.0 ' = 2^8 + 4^8 + 6^8 + ... + 5^8 + 0^8 24678051.0 ' = 2^8 + 4^8 + 6^8 + ... + 5^8 + 1^8 88593477.0 ' = 8^8 + 8^8 + 5^8 + ... + 7^8 + 7^8 3435.00000 3435 = 3^3 + 4^4 + 3^3 + 5^5 _________________________________________________________________ 136.000000 136 = 2^3 + 4^3 + 4^3 244.000000 244 = 1^3 + 3^3 + 6^3 2178.00000 2178 = 6^4 + 5^4 + 1^4 + 4^4 6514.00000 6514 = 2^4 + 1^4 + 7^4 + 8^4 _________________________________________________________________ 504.000000 504 = 12 * 42 = 24 * 21 756.000000 756 = 12 * 63 = 36 * 21 806.000000 806 = 13 * 62 = 26 * 31 1008.00000 1008 = 12 * 84 = 48 * 21 1148.00000 1148 = 14 * 82 = 28 * 41 1209.00000 1209 = 13 * 93 = 39 * 31 1472.00000 1472 = 23 * 64 = 46 * 32 1512.00000 1512 = 24 * 63 = 36 * 42 2208.00000 2178 = 23 * 96 = 69 * 32 2416.00000 2416 = 24 * 84 = 48 * 42 2418.00000 2418 = 26 * 93 = 39 * 62 2924.00000 2924 = 34 * 86 = 68 * 43 3024.00000 3024 = 36 * 84 = 48 * 63 4416.00000 4416 = 46 * 96 = 69 * 64 _________________________________________________________________ 144.000000 144 = 12^2 441.000000 441 = 21^2 169.000000 169 = 13^2 961.000000 961 = 31^2 _________________________________________________________________ 1233.00000 1233 = 12^2 + 33^2 8833.00000 8833 = 88^2 + 33^2 _________________________________________________________________ 8712.00000 8712 = 2178 * 4 9801.00000 9801 = 1089 * 9 = 99^2 _________________________________________________________________ 2592.00000 2592 = 2^5 * 9^2 _________________________________________________________________ 145.000000 145 = 1! + 4! + 5! 40585.0000 = 4! + 0! + 5! + 8! + 5! _________________________________________________________________ 18.0000000 ' 18 = 3 * 6 = 3 + 4 + 5 + 6 525.000000 ' 525 = 15 * 35 = 15 + ... + 34 + 35 17340.0000 ' = 85 * 204 = 85 + ... + 203 + 204 586177.000 ' = 493 * 1189 = 493 + ... + 1188 + 1189 19896030.0 ' = 2871 * 6930 = 2871 + ... + 6929 + 6930 _________________________________________________________________ 15.0000000 15 = 1 + 2 + 3 + 4 + 5 27.0000000 27 = 2 + 3 + 4 + 5 + 6 + 7 429.000000 ' 429 = 4 + 5 + 6 + ... + 28 + 29 1353.00000 ' 1353 = 13 + 14 + 15 + ... + 52 + 53 1863.00000 ' 1863 = 18 + 19 + 20 + ... + 62 + 63 3388.00000 ' 3388 = 33 + 34 + 35 + ... + 87 + 88 3591.00000 ' 3591 = 35 + 36 + 37 + ... + 90 + 91 _________________________________________________________________ 6.00000000 6 = 1 * 2 * 3 24.0000000 24 = 2 * 3 * 4 60.0000000 60 = 3 * 4 * 5 120.000000 120 = 4 * 5 * 6 210.000000 210 = 5 * 6 * 7 336.000000 336 = 6 * 7 * 8 504.000000 504 = 7 * 8 * 9 720.000000 720 = 8 * 9 * 10 990.000000 990 = 9 * 10 * 11 1320.00000 1320 = 10 * 11 * 12 1716.00000 1716 = 11 * 12 * 13 2184.00000 2184 = 12 * 13 * 14 2730.00000 2730 = 13 * 14 * 15 3360.00000 3360 = 14 * 15 * 16 4080.00000 4080 = 15 * 16 * 17 4896.00000 4896 = 16 * 17 * 18 5814.00000 5814 = 17 * 18 * 19 6840.00000 6840 = 18 * 19 * 20 7980.00000 7980 = 19 * 20 * 21 9240.00000 9240 = 20 * 21 * 22 _________________________________________________________________ 5.00000000 5 = 1 + 4 = 2 + 3 6.00000000 6 = 1 + 5 = 2 + 4 8.00000000 8 = 1 + 7 = 2 + 6 14.0000000 14 = 5 + 9 = 6 + 8 15.0000000 15 = 6 + 9 = 7 + 8 65.0000000 65 = 1^2 + 8^2 = 4^2 + 7^2 85.0000000 85 = 2^2 + 9^2 = 6^2 + 7^2 7.00000000 7 = 1 + 6 = 2 + 5 = 3 + 4 12.0000000 12 = 3 + 9 = 4 + 8 = 5 + 7 13.0000000 13 = 4 + 9 = 5 + 8 = 6 + 7 11.0000000 11 = 1 + 3 + 7 = 2 + 4 + 5 12.0000000 12 = 1 + 2 + 9 = 3 + 4 + 5 13.0000000 13 = 1 + 3 + 9 = 2 + 4 + 7 14.0000000 14 = 1 + 4 + 9 = 2 + 5 + 7 15.0000000 15 = 1 + 5 + 9 = 2 + 6 + 7 16.0000000 16 = 1 + 6 + 9 = 3 + 5 + 8 17.0000000 17 = 1 + 7 + 9 = 3 + 6 + 8 18.0000000 18 = 1 + 8 + 9 = 5 + 6 + 7 19.0000000 19 = 3 + 7 + 9 = 5 + 6 + 8 62.0000000 62 = 1^2 + 5^2 + 6^2 = 2^2 + 3^2 + 7^2 77.0000000 77 = 2^2 + 3^2 + 8^2 = 4^2 + 5^2 + 6^2 89.0000000 89 = 2^2 + 6^2 + 7^2 = 3^2 + 4^2 + 8^2 98.0000000 98 = 1^2 + 4^2 + 9^2 = 3^2 + 5^2 + 8^2 101.000000 101 = 1^2 + 6^2 + 8^2 = 2^2 + 4^2 + 9^2 122.000000 122 = 3^2 + 7^2 + 8^2 = 4^2 + 5^2 + 9^2 6578.00000 6578 = 1^4 + 2^4 + 9^4 = 3^4 + 7^4 + 8^4 9.00000000 9 = 1 + 8 = 2 + 7 = 3 + 6 = 4 + 5 10.0000000 10 = 1 + 9 = 2 + 8 = 3 + 7 = 4 + 6 11.0000000 11 = 2 + 9 = 3 + 8 = 4 + 7 = 5 + 6 18.0000000 ' 18 = 1 + 2 + 7 + 8 = 3 + 4 + 5 + 6 19.0000000 ' 19 = 1 + 3 + 6 + 9 = 2 + 4 + 5 + 8 20.0000000 ' 20 = 1 + 2 + 8 + 9 = 3 + 4 + 6 + 7 21.0000000 ' 21 = 1 + 4 + 7 + 9 = 2 + 5 + 6 + 8 22.0000000 ' 22 = 2 + 3 + 8 + 9 = 4 + 5 + 6 + 7 102.000000 ' 102 = 1^2 + 4^2 + 6^2 + 7^2 = 2^2 + 3^2 + 5^2 + 8^2 130.000000 ' 130 = 1^2 + 4^2 + 7^2 + 8^2 = 2^2 + 3^2 + 6^2 + 9^2 142.000000 ' 142 = 2^2 + 5^2 + 7^2 + 8^2 = 3^2 + 4^2 + 6^2 + 9^2 _________________________________________________________________ 1.00000000 1 = 1! 2.00000000 2 = 2! = 1 * 2 6.00000000 6 = 3! = 1 * 2 * 3 24.0000000 24 = 4! = 1 * 2 * 3 * 4 120.000000 120 = 5! = 1 * 2 * 3 * 4 * 5 720.000000 720 = 6! = 1 * 2 * ... * 5 * 6 5040.00000 5040 = 7! = 1 * 2 * ... * 6 * 7 .... _________________________________________________________________ 1.00000000 1 = 1! 3.00000000 3 = 1! + 2! 9.00000000 9 = 1! + 2! + 3! 33.0000000 33 = 1! + 2! + 3! + 4! 153.000000 153 = 1! + 2! + 3! + 4! + 5! 873.000000 873 = 1! + 2! + 3! + 4! + 5! + 6! 5913.00000 5913 = 1! + 2! + 3! + ... + 6! + 7! .... _________________________________________________________________ 1.00000000 1 = 1!^2 5.00000000 5 = 1!^2 + 2!^2 41.0000000 41 = 1!^2 + 2!^2 + 3!^2 617.000000 617 = 1!^2 + 2!^2 + 3!^2 + 4!^2 15017.0000 = 1!^2 + 2!^2 + 3!^2 + 4!^2 + 5!^2 533417.000 = 1!^2 + 2!^2 + 3!^2 + 4!^2 + 5!^2 + 6!^2 .... _________________________________________________________________ 1.00000000 1 = 1!^3 9.00000000 9 = 1!^3 + 2!^3 225.000000 225 = 1!^3 + 2!^3 + 3!^3 14049.0000 = 1!^3 + 2!^3 + 3!^3 + 4!^3 1742049.00 = 1!^3 + 2!^3 + 3!^3 + 4!^3 + 5!^3 374990049. = 1!^3 + 2!^3 + 3!^3 + 4!^3 + 5!^3 + 6!^3 .... _________________________________________________________________ 1.00000000 1 = 1!^4 17.0000000 17 = 1!^4 + 2!^4 1313.00000 1313 = 1!^4 + 2!^4 + 3!^4 333089.000 = 1!^4 + 2!^4 + 3!^4 + 4!^4 207693089. = 1!^4 + 2!^4 + 3!^4 + 4!^4 + 5!^4 .... _________________________________________________________________ 1.00000000 1 = 1!^5 33.0000000 33 = 1!^5 + 2!^5 7809.00000 7809 = 1!^5 + 2!^5 + 3!^5 7970433.00 = 1!^5 + 2!^5 + 3!^5 + 4!^5 .... _________________________________________________________________ 1.00000000 1 = 1 3.00000000 3 = 1 + 2 6.00000000 6 = 1 + 2 + 3 10.0000000 10 = 1 + 2 + 3 + 4 15.0000000 15 = 1 + 2 + 3 + 4 + 5 21.0000000 21 = 1 + 2 + 3 + 4 + 5 + 6 28.0000000 28 = 1 + 2 + 3 + ... + 6 + 7 36.0000000 36 = 1 + 2 + 3 + ... + 7 + 8 45.0000000 45 = 1 + 2 + 3 + ... + 8 + 9 55.0000000 55 = 1 + 2 + 3 + ... + 9 + 10 66.0000000 66 = 1 + 2 + 3 + ... + 10 + 11 78.0000000 78 = 1 + 2 + 3 + ... + 11 + 12 91.0000000 91 = 1 + 2 + 3 + ... + 12 + 13 105.000000 105 = 1 + 2 + 3 + ... + 13 + 14 120.000000 120 = 1 + 2 + 3 + ... + 14 + 15 136.000000 136 = 1 + 2 + 3 + ... + 15 + 16 153.000000 153 = 1 + 2 + 3 + ... + 16 + 17 171.000000 171 = 1 + 2 + 3 + ... + 17 + 18 190.000000 190 = 1 + 2 + 3 + ... + 18 + 19 210.000000 210 = 1 + 2 + 3 + ... + 19 + 20 231.000000 231 = 1 + 2 + 3 + ... + 20 + 21 253.000000 253 = 1 + 2 + 3 + ... + 21 + 22 276.000000 276 = 1 + 2 + 3 + ... + 22 + 23 300.000000 300 = 1 + 2 + 3 + ... + 23 + 24 325.000000 325 = 1 + 2 + 3 + ... + 24 + 25 351.000000 351 = 1 + 2 + 3 + ... + 25 + 26 378.000000 378 = 1 + 2 + 3 + ... + 26 + 27 406.000000 406 = 1 + 2 + 3 + ... + 27 + 28 435.000000 435 = 1 + 2 + 3 + ... + 28 + 29 465.000000 465 = 1 + 2 + 3 + ... + 29 + 30 496.000000 496 = 1 + 2 + 3 + ... + 30 + 31 528.000000 528 = 1 + 2 + 3 + ... + 31 + 32 561.000000 561 = 1 + 2 + 3 + ... + 32 + 33 595.000000 595 = 1 + 2 + 3 + ... + 33 + 34 630.000000 630 = 1 + 2 + 3 + ... + 34 + 35 666.000000 666 = 1 + 2 + 3 + ... + 35 + 36 703.000000 703 = 1 + 2 + 3 + ... + 36 + 37 741.000000 741 = 1 + 2 + 3 + ... + 37 + 38 780.000000 780 = 1 + 2 + 3 + ... + 38 + 39 820.000000 820 = 1 + 2 + 3 + ... + 39 + 40 861.000000 861 = 1 + 2 + 3 + ... + 40 + 41 903.000000 903 = 1 + 2 + 3 + ... + 41 + 42 946.000000 946 = 1 + 2 + 3 + ... + 42 + 43 990.000000 990 = 1 + 2 + 3 + ... + 43 + 44 1035.00000 1035 = 1 + 2 + 3 + ... + 44 + 45 1081.00000 1081 = 1 + 2 + 3 + ... + 45 + 46 1128.00000 1128 = 1 + 2 + 3 + ... + 46 + 47 1176.00000 1176 = 1 + 2 + 3 + ... + 47 + 48 1225.00000 1225 = 1 + 2 + 3 + ... + 48 + 49 1275.00000 1275 = 1 + 2 + 3 + ... + 49 + 50 1326.00000 1326 = 1 + 2 + 3 + ... + 50 + 51 1378.00000 1378 = 1 + 2 + 3 + ... + 51 + 52 1431.00000 1431 = 1 + 2 + 3 + ... + 52 + 53 1485.00000 1485 = 1 + 2 + 3 + ... + 53 + 54 1540.00000 1540 = 1 + 2 + 3 + ... + 54 + 55 1596.00000 1596 = 1 + 2 + 3 + ... + 55 + 56 1653.00000 1653 = 1 + 2 + 3 + ... + 56 + 57 1711.00000 1711 = 1 + 2 + 3 + ... + 57 + 58 1770.00000 1770 = 1 + 2 + 3 + ... + 58 + 59 1830.00000 1830 = 1 + 2 + 3 + ... + 59 + 60 1891.00000 1891 = 1 + 2 + 3 + ... + 60 + 61 1953.00000 1953 = 1 + 2 + 3 + ... + 61 + 62 2016.00000 2016 = 1 + 2 + 3 + ... + 62 + 63 2080.00000 2080 = 1 + 2 + 3 + ... + 63 + 64 2145.00000 2145 = 1 + 2 + 3 + ... + 64 + 65 2211.00000 2211 = 1 + 2 + 3 + ... + 65 + 66 2278.00000 2278 = 1 + 2 + 3 + ... + 66 + 67 2346.00000 2346 = 1 + 2 + 3 + ... + 67 + 68 2415.00000 2415 = 1 + 2 + 3 + ... + 68 + 69 2485.00000 2485 = 1 + 2 + 3 + ... + 69 + 70 2556.00000 2556 = 1 + 2 + 3 + ... + 70 + 71 2628.00000 2628 = 1 + 2 + 3 + ... + 71 + 72 2701.00000 2701 = 1 + 2 + 3 + ... + 72 + 73 2775.00000 2775 = 1 + 2 + 3 + ... + 73 + 74 2850.00000 2850 = 1 + 2 + 3 + ... + 74 + 75 2926.00000 2926 = 1 + 2 + 3 + ... + 75 + 76 3003.00000 3003 = 1 + 2 + 3 + ... + 76 + 77 3081.00000 3081 = 1 + 2 + 3 + ... + 77 + 78 3160.00000 3160 = 1 + 2 + 3 + ... + 78 + 79 3240.00000 3240 = 1 + 2 + 3 + ... + 79 + 80 3321.00000 3321 = 1 + 2 + 3 + ... + 80 + 81 3403.00000 3403 = 1 + 2 + 3 + ... + 81 + 82 3486.00000 3486 = 1 + 2 + 3 + ... + 82 + 83 3570.00000 3570 = 1 + 2 + 3 + ... + 83 + 84 3655.00000 3655 = 1 + 2 + 3 + ... + 84 + 85 3741.00000 3741 = 1 + 2 + 3 + ... + 85 + 86 3828.00000 3828 = 1 + 2 + 3 + ... + 86 + 87 3916.00000 3916 = 1 + 2 + 3 + ... + 87 + 88 4005.00000 4005 = 1 + 2 + 3 + ... + 88 + 89 4095.00000 4095 = 1 + 2 + 3 + ... + 89 + 90 4186.00000 4186 = 1 + 2 + 3 + ... + 90 + 91 4278.00000 4278 = 1 + 2 + 3 + ... + 91 + 92 4371.00000 4371 = 1 + 2 + 3 + ... + 92 + 93 4465.00000 4465 = 1 + 2 + 3 + ... + 93 + 94 4560.00000 4560 = 1 + 2 + 3 + ... + 94 + 95 4656.00000 4656 = 1 + 2 + 3 + ... + 95 + 96 4753.00000 4753 = 1 + 2 + 3 + ... + 96 + 97 4851.00000 4851 = 1 + 2 + 3 + ... + 97 + 98 4950.00000 4950 = 1 + 2 + 3 + ... + 98 + 99 5050.00000 5050 = 1 + 2 + 3 + ... + 99 + 100 5151.00000 5151 = 1 + 2 + 3 + ... + 100 + 101 5253.00000 5253 = 1 + 2 + 3 + ... + 101 + 102 5356.00000 5356 = 1 + 2 + 3 + ... + 102 + 103 5460.00000 5460 = 1 + 2 + 3 + ... + 103 + 104 5565.00000 5565 = 1 + 2 + 3 + ... + 104 + 105 5671.00000 5671 = 1 + 2 + 3 + ... + 105 + 106 5778.00000 5778 = 1 + 2 + 3 + ... + 106 + 107 5886.00000 5886 = 1 + 2 + 3 + ... + 107 + 108 5995.00000 5995 = 1 + 2 + 3 + ... + 108 + 109 6105.00000 6105 = 1 + 2 + 3 + ... + 109 + 110 6216.00000 6216 = 1 + 2 + 3 + ... + 110 + 111 6328.00000 6328 = 1 + 2 + 3 + ... + 111 + 112 6441.00000 6441 = 1 + 2 + 3 + ... + 112 + 113 6555.00000 6555 = 1 + 2 + 3 + ... + 113 + 114 6670.00000 6670 = 1 + 2 + 3 + ... + 114 + 115 6786.00000 6786 = 1 + 2 + 3 + ... + 115 + 116 6903.00000 6903 = 1 + 2 + 3 + ... + 116 + 117 7021.00000 7021 = 1 + 2 + 3 + ... + 117 + 118 7140.00000 7140 = 1 + 2 + 3 + ... + 118 + 119 7260.00000 7260 = 1 + 2 + 3 + ... + 119 + 120 7381.00000 7381 = 1 + 2 + 3 + ... + 120 + 121 7503.00000 7503 = 1 + 2 + 3 + ... + 121 + 122 7626.00000 7626 = 1 + 2 + 3 + ... + 122 + 123 7750.00000 7750 = 1 + 2 + 3 + ... + 123 + 124 7875.00000 7875 = 1 + 2 + 3 + ... + 124 + 125 8001.00000 8001 = 1 + 2 + 3 + ... + 125 + 126 8128.00000 8128 = 1 + 2 + 3 + ... + 126 + 127 8256.00000 8256 = 1 + 2 + 3 + ... + 127 + 128 8385.00000 8385 = 1 + 2 + 3 + ... + 128 + 129 8515.00000 8515 = 1 + 2 + 3 + ... + 129 + 130 8646.00000 8646 = 1 + 2 + 3 + ... + 130 + 131 8778.00000 8778 = 1 + 2 + 3 + ... + 131 + 132 8911.00000 8911 = 1 + 2 + 3 + ... + 132 + 133 9045.00000 9045 = 1 + 2 + 3 + ... + 133 + 134 9180.00000 9180 = 1 + 2 + 3 + ... + 134 + 135 9316.00000 9316 = 1 + 2 + 3 + ... + 135 + 136 9453.00000 9453 = 1 + 2 + 3 + ... + 136 + 137 9591.00000 9591 = 1 + 2 + 3 + ... + 137 + 138 9730.00000 9730 = 1 + 2 + 3 + ... + 138 + 139 9870.00000 9870 = 1 + 2 + 3 + ... + 139 + 140 .... _________________________________________________________________ 1.00000000 1 = 1^2 5.00000000 5 = 1^2 + 2^2 14.0000000 14 = 1^2 + 2^2 + 3^2 30.0000000 30 = 1^2 + 2^2 + 3^2 + 4^2 55.0000000 55 = 1^2 + 2^2 + 3^2 + 4^2 + 5^2 91.0000000 91 = 1^2 + 2^2 + 3^2 + 4^2 + 5^2 + 6^2 140.000000 140 = 1^2 + 2^2 + 3^2 + ... + 6^2 + 7^2 204.000000 204 = 1^2 + 2^2 + 3^2 + ... + 7^2 + 8^2 285.000000 285 = 1^2 + 2^2 + 3^2 + ... + 8^2 + 9^2 385.000000 385 = 1^2 + 2^2 + 3^2 + ... + 9^2 + 10^2 506.000000 506 = 1^2 + 2^2 + 3^2 + ... + 10^2 + 11^2 650.000000 650 = 1^2 + 2^2 + 3^2 + ... + 11^2 + 12^2 819.000000 819 = 1^2 + 2^2 + 3^2 + ... + 12^2 + 13^2 1015.00000 1015 = 1^2 + 2^2 + 3^2 + ... + 13^2 + 14^2 1240.00000 1240 = 1^2 + 2^2 + 3^2 + ... + 14^2 + 15^2 1496.00000 1496 = 1^2 + 2^2 + 3^2 + ... + 15^2 + 16^2 1785.00000 1785 = 1^2 + 2^2 + 3^2 + ... + 16^2 + 17^2 2109.00000 2109 = 1^2 + 2^2 + 3^2 + ... + 17^2 + 18^2 2470.00000 2470 = 1^2 + 2^2 + 3^2 + ... + 18^2 + 19^2 2870.00000 2870 = 1^2 + 2^2 + 3^2 + ... + 19^2 + 20^2 3311.00000 3311 = 1^2 + 2^2 + 3^2 + ... + 20^2 + 21^2 3795.00000 3795 = 1^2 + 2^2 + 3^2 + ... + 21^2 + 22^2 4324.00000 4324 = 1^2 + 2^2 + 3^2 + ... + 22^2 + 23^2 4900.00000 4900 = 1^2 + 2^2 + 3^2 + ... + 23^2 + 24^2 5525.00000 5525 = 1^2 + 2^2 + 3^2 + ... + 24^2 + 25^2 6201.00000 6201 = 1^2 + 2^2 + 3^2 + ... + 25^2 + 26^2 6930.00000 6930 = 1^2 + 2^2 + 3^2 + ... + 26^2 + 27^2 7714.00000 7714 = 1^2 + 2^2 + 3^2 + ... + 27^2 + 28^2 8555.00000 8555 = 1^2 + 2^2 + 3^2 + ... + 28^2 + 29^2 9455.00000 9455 = 1^2 + 2^2 + 3^2 + ... + 29^2 + 30^2 .... _________________________________________________________________ 1.00000000 1 = 1^3 9.00000000 9 = 1^3 + 2^3 36.0000000 36 = 1^3 + 2^3 + 3^3 100.000000 100 = 1^3 + 2^3 + 3^3 + 4^3 225.000000 225 = 1^3 + 2^3 + 3^3 + 4^3 + 5^3 441.000000 441 = 1^3 + 2^3 + 3^3 + 4^3 + 5^3 + 6^3 784.000000 784 = 1^3 + 2^3 + 3^3 + ... + 6^3 + 7^3 1296.00000 1296 = 1^3 + 2^3 + 3^3 + ... + 7^3 + 8^3 2025.00000 2025 = 1^3 + 2^3 + 3^3 + ... + 8^3 + 9^3 3025.00000 3025 = 1^3 + 2^3 + 3^3 + ... + 9^3 + 10^3 4356.00000 4356 = 1^3 + 2^3 + 3^3 + ... + 10^3 + 11^3 6084.00000 6084 = 1^3 + 2^3 + 3^3 + ... + 11^3 + 12^3 8281.00000 8281 = 1^3 + 2^3 + 3^3 + ... + 12^3 + 13^3 .... _________________________________________________________________ 1.00000000 1 = 1^4 17.0000000 17 = 1^4 + 2^4 98.0000000 98 = 1^4 + 2^4 + 3^4 354.000000 354 = 1^4 + 2^4 + 3^4 + 4^4 979.000000 979 = 1^4 + 2^4 + 3^4 + 4^4 + 5^4 2275.00000 2275 = 1^4 + 2^4 + 3^4 + 4^4 + 5^4 + 6^4 4676.00000 4676 = 1^4 + 2^4 + 3^4 + ... + 6^4 + 7^4 8772.00000 8772 = 1^4 + 2^4 + 3^4 + ... + 7^4 + 8^4 .... _________________________________________________________________ 1.00000000 1 = 1^5 33.0000000 33 = 1^5 + 2^5 276.000000 276 = 1^5 + 2^5 + 3^5 1300.00000 1300 = 1^5 + 2^5 + 3^5 + 4^5 4425.00000 4425 = 1^5 + 2^5 + 3^5 + 4^5 + 5^5 12201.0000 = 1^5 + 2^5 + 3^5 + 4^5 + 5^5 + 6^5 .... _________________________________________________________________ 1.00000000 1 = 1^6 65.0000000 65 = 1^6 + 2^6 794.000000 794 = 1^6 + 2^6 + 3^6 4890.00000 4890 = 1^6 + 2^6 + 3^6 + 4^6 20515.0000 = 1^6 + 2^6 + 3^6 + 4^6 + 5^6 67171.0000 = 1^6 + 2^6 + 3^6 + 4^6 + 5^6 + 6^6 .... _________________________________________________________________ 1.00000000 1 = 1^7 129.000000 129 = 1^7 + 2^7 2316.00000 2316 = 1^7 + 2^7 + 3^7 18700.0000 = 1^7 + 2^7 + 3^7 + 4^7 96825.0000 = 1^7 + 2^7 + 3^7 + 4^7 + 5^7 376761.000 = 1^7 + 2^7 + 3^7 + 4^7 + 5^7 + 6^7 .... _________________________________________________________________ 1.00000000 1 = 1^8 257.000000 257 = 1^8 + 2^8 6818.00000 6818 = 1^8 + 2^8 + 3^8 72354.0000 = 1^8 + 2^8 + 3^8 + 4^8 462979.000 = 1^8 + 2^8 + 3^8 + 4^8 + 5^8 2142595.00 = 1^8 + 2^8 + 3^8 + 4^8 + 5^8 + 6^8 .... _________________________________________________________________ 1.00000000 1 = 1^9 513.000000 513 = 1^9 + 2^9 20196.0000 = 1^9 + 2^9 + 3^9 282340.000 = 1^9 + 2^9 + 3^9 + 4^9 2235465.00 = 1^9 + 2^9 + 3^9 + 4^9 + 5^9 12343161.0 = 1^9 + 2^9 + 3^9 + 4^9 + 5^9 + 6^9 .... _________________________________________________________________ 1.00000000 1 = 1 5.00000000 5 = 1 + 2^2 32.0000000 32 = 1 + 2^2 + 3^3 288.000000 288 = 1 + 2^2 + 3^3 + 4^4 3413.00000 3413 = 1 + 2^2 + 3^3 + 4^4 + 5^5 50069.0000 = 1 + 2^2 + 3^3 + 4^4 + 5^5 + 6^6 .... ^(")^
