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реферат на тему: Сумма делителей числа

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Сумма делителей числа. Для начало приведём экспериментальный материал (который был получен с помощью программы Derive (по формуле 1.(см.ниже)): для нахождения делителей числа «a», программа делила число «a» на другие числа не превосходящие само число и если остаток от деления был равен 0, то число записывалось как делитель «a». ): Ниже приведены все делители чисел от 1 до 1000:[1, [1]] [2, [1, 2]] [3, [1, 3]] [4, [1, 2, 4]] [5, [1, 5]] [6, [1, 2, 3, 6]] [7, [1, 7]] [8, [1, 2, 4, 8]] [9, [1, 3, 9]] [10, [1, 2, 5, 10]] [11, [1, 11]] [12, [1, 2, 3, 4, 6, 12]] [13, [1, 13]] [14, [1, 2, 7, 14]] [15, [1, 3, 5, 15]] [16, [1, 2, 4, 8, 16]] [17, [1, 17]] [18, [1, 2, 3, 6, 9, 18]] [19, [1, 19]] [20, [1, 2, 4, 5, 10, 20]] [21, [1, 3, 7, 21]] [22, [1, 2, 11, 22]] [23, [1, 23]] [24, [1, 2, 3, 4, 6, 8, 12, 24]] [25, [1, 5, 25]] [26, [1, 2, 13, 26]] [27, [1, 3, 9, 27]] [28, [1, 2, 4, 7, 14, 28]] [29, [1, 29]] [30, [1, 2, 3, 5, 6, 10, 15, 30]] [31, [1, 31]] [32, [1, 2, 4, 8, 16, 32]] [33, [1, 3, 11, 33]] [34, [1, 2, 17, 34]] [35, [1, 5, 7, 35]] [36, [1, 2, 3, 4, 6, 9, 12, 18, 36]] [37, [1, 37]] [38, [1, 2, 19, 38]] [39, [1, 3, 13, 39]] [40, [1, 2, 4, 5, 8, 10, 20, 40]] [41, [1, 41]] [42, [1, 2, 3, 6, 7, 14, 21, 42]] [43, [1, 43]] [44, [1, 2, 4, 11, 22, 44]] [45, [1, 3, 5, 9, 15, 45]] [46, [1, 2, 23, 46]] [47, [1, 47]] [48, [1, 2, 3, 4, 6, 8, 12, 16, 24, 48]] [49, [1, 7, 49]] [50, [1, 2, 5, 10, 25, 50]] [51, [1, 3, 17, 51]] [52, [1, 2, 4, 13, 26, 52]] [53, [1, 53]] [54, [1, 2, 3, 6, 9, 18, 27, 54]] [55, [1, 5, 11, 55]] [56, [1, 2, 4, 7, 8, 14, 28, 56]] [57, [1, 3, 19, 57]] [58, [1, 2, 29, 58]] [59, [1, 59]] [60, [1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60]] [61, [1, 61]] [62, [1, 2, 31, 62]] [63, [1, 3, 7, 9, 21, 63]] [64, [1, 2, 4, 8, 16, 32, 64]] [65, [1, 5, 13, 65]] [66, [1, 2, 3, 6, 11, 22, 33, 66]] [67, [1, 67]] [68, [1, 2, 4, 17, 34, 68]] [69, [1, 3, 23, 69]] [70, [1, 2, 5, 7, 10, 14, 35, 70]] [71, [1, 71]] [72, [1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72]] [73, [1, 73]] [74, [1, 2, 37, 74]] [75, [1, 3, 5, 15, 25, 75]] [76, [1, 2, 4, 19, 38, 76]] [77, [1, 7, 11, 77]] [78, [1, 2, 3, 6, 13, 26, 39, 78]] [79, [1, 79]] [80, [1, 2, 4, 5, 8, 10, 16, 20, 40, 80]] [81, [1, 3, 9, 27, 81]] [82, [1, 2, 41, 82]] [83, [1, 83]] [84, [1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84]] [85, [1, 5, 17, 85]] [86, [1, 2, 43, 86]] [87, [1, 3, 29, 87]] [88, [1, 2, 4, 8, 11, 22, 44, 88]] [89, [1, 89]] [90, [1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90]] [91, [1, 7, 13, 91]] [92, [1, 2, 4, 23, 46, 92]] [93, [1, 3, 31, 93]] [94, [1, 2, 47, 94]] [95, [1, 5, 19, 95]] [96, [1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96]] [97, [1, 97]] [98, [1, 2, 7, 14, 49, 98]] [99, [1, 3, 9, 11, 33, 99]] [100, [1, 2, 4, 5, 10, 20, 25, 50, 100]] [101, [1, 101]] [102, [1, 2, 3, 6, 17, 34, 51, 102]] [103, [1, 103]] [104, [1, 2, 4, 8, 13, 26, 52, 104]] [105, [1, 3, 5, 7, 15, 21, 35, 105]] [106, [1, 2, 53, 106]] [107, [1, 107]] [108, [1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108]] [109, [1, 109]] [110, [1, 2, 5, 10, 11, 22, 55, 110]] [111, [1, 3, 37, 111]] [112, [1, 2, 4, 7, 8, 14, 16, 28, 56, 112]] [113, [1, 113]] [114, [1, 2, 3, 6, 19, 38, 57, 114]] [115, [1, 5, 23, 115]] [116, [1, 2, 4, 29, 58, 116]] [117, [1, 3, 9, 13, 39, 117]] [118, [1, 2, 59, 118]] [119, [1, 7, 17, 119]] [120, [1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120]] [121, [1, 11, 121]] [122, [1, 2, 61, 122]] [123, [1, 3, 41, 123]] [124, [1, 2, 4, 31, 62, 124]] [125, [1, 5, 25, 125]] [126, [1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63,
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126]] [127, [1, 127]] [128, [1, 2, 4, 8, 16, 32, 64, 128]] [129, [1, 3, 43, 129]] [130, [1, 2, 5, 10, 13, 26, 65, 130]] [131, [1, 131]] [132, [1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132]] [133, [1, 7, 19, 133]] [134, [1, 2, 67, 134]] [135, [1, 3, 5, 9, 15, 27, 45, 135]] [136, [1, 2, 4, 8, 17, 34, 68, 136]] [137, [1, 137]] [138, [1, 2, 3, 6, 23, 46, 69, 138]] [139, [1, 139]] [140, [1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140]] [141, [1, 3, 47, 141]] [142, [1, 2, 71, 142]] [143, [1, 11, 13, 143]] [144, [1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144]] [145, [1, 5, 29, 145]] [146, [1, 2, 73, 146]] [147, [1, 3, 7, 21, 49, 147]] [148, [1, 2, 4, 37, 74, 148]] [149, [1, 149]] [150, [1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150]] [151, [1, 151]] [152, [1, 2, 4, 8, 19, 38, 76, 152]] [153, [1, 3, 9, 17, 51, 153]] [154, [1, 2, 7, 11, 14, 22, 77, 154]] [155, [1, 5, 31, 155]] [156, [1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 156]] [157, [1, 157]] [158, [1, 2, 79, 158]] [159, [1, 3, 53, 159]] [160, [1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 160]] [161, [1, 7, 23, 161]] [162, [1, 2, 3, 6, 9, 18, 27, 54, 81, 162]] [163, [1, 163]] [164, [1, 2, 4, 41, 82, 164]] [165, [1, 3, 5, 11, 15, 33, 55, 165]] [166, [1, 2, 83, 166]] [167, [1, 167]] [168, [1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168]] [169, [1, 13, 169]] [170, [1, 2, 5, 10, 17, 34, 85, 170]] [171, [1, 3, 9, 19, 57, 171]] [172, [1, 2, 4, 43, 86, 172]] [173, [1, 173]] [174, [1, 2, 3, 6, 29, 58, 87, 174]] [175, [1, 5, 7, 25, 35, 175]] [176, [1, 2, 4, 8, 11, 16, 22, 44, 88, 176]] [177, [1, 3, 59, 177]] [178, [1, 2, 89, 178]] [179, [1, 179]] [180, [1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180]] [181, [1, 181]] [182, [1, 2, 7, 13, 14, 26, 91, 182]] [183, [1, 3, 61, 183]] [184, [1, 2, 4, 8, 23, 46, 92, 184]] [185, [1, 5, 37, 185]] [186, [1, 2, 3, 6, 31, 62, 93, 186]] [187, [1, 11, 17, 187]] [188, [1, 2, 4, 47, 94, 188]] [189, [1, 3, 7, 9, 21, 27, 63, 189]] [190, [1, 2, 5, 10, 19, 38, 95, 190]] [191, [1, 191]] [192, [1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192]] [193, [1, 193]] [194, [1, 2, 97, 194]] [195, [1, 3, 5, 13, 15, 39, 65, 195]] [196, [1, 2, 4, 7, 14, 28, 49, 98, 196]] [197, [1, 197]] [198, [1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, 198]] [199, [1, 199]] [200, [1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200]] [201, [1, 3, 67, 201]] [202, [1, 2, 101, 202]] [203, [1, 7, 29, 203]] [204, [1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, 204]] [205, [1, 5, 41, 205]] [206, [1, 2, 103, 206]] [207, [1, 3, 9, 23, 69, 207]] [208, [1, 2, 4, 8, 13, 16, 26, 52, 104, 208]] [209, [1, 11, 19, 209]] [210, [1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210]] [211, [1, 211]] [212, [1, 2, 4, 53, 106, 212]] [213, [1, 3, 71, 213]] [214, [1, 2, 107, 214]] [215, [1, 5, 43, 215]] [216, [1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216]] [217, [1, 7, 31, 217]] [218, [1, 2, 109, 218]] [219, [1, 3, 73, 219]] [220, [1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110, 220]] [221, [1, 13, 17, 221]] [222, [1, 2, 3, 6, 37, 74, 111, 222]] [223, [1, 223]] [224, [1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, 224]] [225, [1, 3, 5, 9, 15, 25, 45, 75, 225]] [226, [1, 2, 113, 226]] [227, [1, 227]] [228, [1, 2, 3, 4, 6, 12, 19, 38, 57, 76, 114, 228]] [229, [1, 229]] [230, [1, 2, 5, 10, 23, 46, 115, 230]] [231, [1, 3, 7, 11, 21, 33, 77, 231]] [232, [1, 2, 4, 8, 29, 58, 116, 232]] [233, [1, 233]] [234, [1, 2, 3, 6, 9, 13, 18, 26, 39, 78, 117, 234]] [235, [1, 5, 47, 235]] [236, [1, 2, 4, 59, 118, 236]] [237,

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