Учебная работа № 1634. 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, 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, [1, 3, 79, 237]]
[238, [1, 2, 7, 14, 17, 34, 119, 238]]
[239, [1, 239]]
[240, [1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240]]
[241, [1, 241]]
[242, [1, 2, 11, 22, 121, 242]]
[243, [1, 3, 9, 27, 81, 243]]
[244, [1, 2, 4, 61, 122, 244]]
[245, [1, 5, 7, 35, 49, 245]]
[246, [1, 2, 3, 6, 41, 82, 123, 246]]
[247, [1, 13, 19, 247]]
[248, [1, 2, 4, 8, 31, 62, 124, 248]]
[249, [1, 3, 83, 249]]
[250, [1, 2, 5, 10, 25, 50, 125, 250]]
[251, [1, 251]]
[252, [1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 252]]
[253, [1, 11, 23, 253]]
[254, [1, 2, 127, 254]]
[255, [1, 3, 5, 15, 17, 51, 85, 255]]
[256, [1, 2, 4, 8, 16, 32, 64, 128, 256]]
[257, [1, 257]]
[258, [1, 2, 3, 6, 43, 86, 129, 258]]
[259, [1, 7, 37, 259]]
[260, [1, 2, 4, 5, 10, 13, 20, 26, 52, 65, 130, 260]]
[261, [1, 3, 9, 29, 87, 261]]
[262, [1, 2, 131, 262]]
[263, [1, 263]]
[264, [1, 2, 3, 4, 6, 8, 11, 12, 22, 24, 33, 44, 66, 88, 132, 264]]
[265, [1, 5, 53, 265]]
[266, [1, 2, 7, 14, 19, 38, 133, 266]]
[267, [1, 3, 89, 267]]
[268, [1, 2, 4, 67, 134, 268]]
[269, [1, 269]]
[270, [1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, 270]]
[271, [1, 271]]
[272, [1, 2, 4, 8, 16, 17, 34, 68, 136, 272]]
[273, [1, 3, 7, 13, 21, 39, 91, 273]]
[274, [1, 2, 137, 274]]
[275, [1, 5, 11, 25, 55, 275]]
[276, [1, 2, 3, 4, 6, 12, 23, 46, 69, 92, 138, 276]]
[277, [1, 277]]
[278, [1, 2, 139, 278]]
[279, [1, 3, 9, 31, 93, 279]]
[280, [1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 56, 70, 140, 280]]
[281, [1, 281]]
[282, [1, 2, 3, 6, 47, 94, 141, 282]]
[283, [1, 283]]
[284, [1, 2, 4, 71, 142, 284]]
[285, [1, 3, 5, 15, 19, 57, 95, 285]]
[286, [1, 2, 11, 13, 22, 26, 143, 286]]
[287, [1, 7, 41, 287]]
[288, [1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 288]]
[289, [1, 17, 289]]
[290, [1, 2, 5, 10, 29, 58, 145, 290]]
[291, [1, 3, 97, 291]]
[292, [1, 2, 4, 73, 146, 292]]
[293, [1, 293]]
[294, [1, 2, 3, 6, 7, 14, 21, 42, 49, 98, 147, 294]]
[295, [1, 5, 59, 295]]
[296, [1, 2, 4, 8, 37, 74, 148, 296]]
[297, [1, 3, 9, 11, 27, 33, 99, 297]]
[298, [1, 2, 149, 298]]
[299, [1, 13, 23, 299]]
[300, [1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300]]
[301, [1, 7, 43, 301]]
[302, [1, 2, 151, 302]]
[303, [1, 3, 101, 303]]
[304, [1, 2, 4, 8, 16, 19, 38, 76, 152, 304]]
[305, [1, 5, 61, 305]]
[306, [1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, 306]]
[307, [1, 307]]
[308, [1, 2, 4, 7, 11, 14, 22, 28, 44, 77, 154, 308]]
[309, [1, 3, 103, 309]]
[310, [1, 2, 5, 10, 31, 62, 155, 310]]
[311, [1, 311]]
[312, [1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312]]
[313, [1, 313]]
[314, [1, 2, 157, 314]]
[315, [1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, 315]]
[316, [1, 2, 4, 79, 158, 316]]
[317, [1, 317]]
[318, [1, 2, 3, 6, 53, 106, 159, 318]]
[319, [1, 11, 29, 319]]
[320, [1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 160, 320]]
[321, [1, 3, 107, 321]]
[322, [1, 2, 7, 14, 23, 46, 161, 322]]
[323, [1, 17, 19, 323]]
[324, [1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 324]]
[325, [1, 5, 13, 25, 65, 325]]
[326, [1, 2, 163, 326]]
[327, [1, 3, 109, 327]]
[328, [1, 2, 4, 8, 41, 82, 164, 328]]
[329, [1, 7, 47, 329]]
[330, [1, 2, 3, 5, 6, 10, 11, 15, 22, 30, 33, 55, 66, 110, 165, 330]]
[331, [1, 331]]
[332, [1, 2, 4, 83, 166, 332]]
[333, [1, 3, 9, 37, 111, 333]]
[334, [1, 2, 167, 334]]
[335, [1, 5, 67, 335]]
[336, [1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56, 84, 112, 168, 336]]
[337, [1, 337]]
[338, [1, 2, 13, 26, 169, 338]]
[339, [1, 3, 113, 339]]
[340, [1, 2, 4, 5, 10, 17, 20, 34, 68, 85, 170, 340]]
[341, [1, 11, 31, 341]]
[342, [1, 2, 3, 6, 9, 18, 19, 38, 57, 114, 171, 342]]
[343, [1, 7, 49, 343]]
[344, [1, 2, 4, 8, 43, 86, 172, 344]]
[345, [1, 3, 5, 15, 23, 69, 115, 345]]
[346, [1, 2, 173, 346]]
[347, [1, 347]]
[348, [1, 2, 3, 4, 6, 12, 29, 58, 87, 116, 174, 348]]
[349, [1, 349]]
[350, [1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 175, 350]]
[351, [1, 3, 9, 13, 27, 39, 117, 351]]
[352, [1, 2, 4, 8, 11, 16, 22, 32, 44, 88, 176, 352]]
[353, [1, 353]]
[354, [1, 2, 3, 6, 59, 118, 177, 354]]
[355, [1, 5, 71, 355]]
[356, [1, 2, 4, 89, 178, 356]]
[357, [1, 3, 7, 17, 21, 51, 119, 357]]
[358, [1, 2, 179, 358]]
[359, [1, 359]]
[360, [1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360]]
[361, [1, 19, 361]]
[362, [1, 2, 181, 362]]
[363, [1, 3, 11, 33, 121, 363]]
[364, [1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 182, 364]]
[365, [1, 5, 73, 365]]
[366, [1, 2, 3, 6, 61, 122, 183, 366]]
[367, [1, 367]]
[368, [1, 2, 4, 8, 16, 23, 46, 92, 184, 368]]
[369, [1, 3, 9, 41, 123, 369]]
[370, [1, 2, 5, 10, 37, 74, 185, 370]]
[371, [1, 7, 53, 371]]
[372, [1, 2, 3, 4, 6, 12, 31, 62, 93, 124, 186, 372]]
[373, [1, 373]]
[374, [1, 2, 11, 17, 22, 34, 187, 374]]
[375, [1, 3, 5, 15, 25, 75, 125, 375]]
[376, [1, 2, 4, 8, 47, 94, 188, 376]]
[377, [1, 13, 29, 377]]
[378, [1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, 378]]
[379, [1, 379]]
[380, [1, 2, 4, 5, 10, 19, 20, 38, 76, 95, 190, 380]]
[381, [1, 3, 127, 381]]
[382, [1, 2, 191, 382]]
[383, [1, 383]]
[384, [1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 384]]
[385, [1, 5, 7, 11, 35, 55, 77, 385]]
[386, [1, 2, 193, 386]]
[387, [1, 3, 9, 43, 129, 387]]
[388, [1, 2, 4, 97, 194, 388]]
[389, [1, 389]]
[390, [1, 2, 3, 5, 6, 10, 13, 15, 26, 30, 39, 65, 78, 130, 195, 390]]
[391, [1, 17, 23, 391]]
[392, [1, 2, 4, 7, 8, 14, 28, 49, 56, 98, 196, 392]]
[393, [1, 3, 131, 393]]
[394, [1, 2, 197, 394]]
[395, [1, 5, 79, 395]]
[396, [1, 2, 3, 4, 6, 9, 11, 12, 18, 22, 33, 36, 44, 66, 99, 132, 198, 396]]
[397, [1, 397]]
[398, [1, 2, 199, 398]]
[399, [1, 3, 7, 19, 21, 57, 133, 399]]
[400, [1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400]]
[401, [1, 401]]
[402, [1, 2, 3, 6, 67, 134, 201, 402]]
[403, [1, 13, 31, 403]]
[404, [1, 2, 4, 101, 202, 404]]
[405, [1, 3, 5, 9, 15, 27, 45, 81, 135, 405]]
[406, [1, 2, 7, 14, 29, 58, 203, 406]]
[407, [1, 11, 37, 407]]
[408, [1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 408]]
[409, [1, 409]]
[410, [1, 2, 5, 10, 41, 82, 205, 410]]
[411, [1, 3, 137, 411]]
[412, [1, 2, 4, 103, 206, 412]]
[413, [1, 7, 59, 413]]
[414, [1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414]]
[415, [1, 5, 83, 415]]
[416, [1, 2, 4, 8, 13, 16, 26, 32, 52, 104, 208, 416]]
[417, [1, 3, 139, 417]]
[418, [1, 2, 11, 19, 22, 38, 209, 418]]
[419, [1, 419]]
[420, [1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420]]
[421, [1, 421]]
[422, [1, 2, 211, 422]]
[423, [1, 3, 9, 47, 141, 423]]
[424, [1, 2, 4, 8, 53, 106, 212, 424]]
[425, [1, 5, 17, 25, 85, 425]]
[426, [1, 2, 3, 6, 71, 142, 213, 426]]
[427, [1, 7, 61, 427]]
[428, [1, 2, 4, 107, 214, 428]]
[429, [1, 3, 11, 13, 33, 39, 143, 429]]
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[804, [1, 2, 3, 4, 6, 12, 67, 134, 201, 268, 402, 804]]
[805, [1, 5, 7, 23, 35, 115, 161, 805]]
[806, [1, 2, 13, 26, 31, 62, 403, 806]]
[807, [1, 3, 269, 807]]
[808, [1, 2, 4, 8, 101, 202, 404, 808]]
[809, [1, 809]]
[810, [1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 135, 162, 270, 405, 810]]
[811, [1, 811]]
[812, [1, 2, 4, 7, 14, 28, 29, 58, 116, 203, 406, 812]]
[813, [1, 3, 271, 813]]
[814, [1, 2, 11, 22, 37, 74, 407, 814]]
[815, [1, 5, 163, 815]]
[816, [1, 2, 3, 4, 6, 8, 12, 16, 17, 24, 34, 48, 51, 68, 102, 136, 204, 272, 408, 816]]
[817, [1, 19, 43, 817]]
[818, [1, 2, 409, 818]]
[819, [1, 3, 7, 9, 13, 21, 39, 63, 91, 117, 273, 819]]
[820, [1, 2, 4, 5, 10, 20, 41, 82, 164, 205, 410, 820]]
[821, [1, 821]]
[822, [1, 2, 3, 6, 137, 274, 411, 822]]
[823, [1, 823]]
[824, [1, 2, 4, 8, 103, 206, 412, 824]]
[825, [1, 3, 5, 11, 15, 25, 33, 55, 75, 165, 275, 825]]
[826, [1, 2, 7, 14, 59, 118, 413, 826]]
[827, [1, 827]]
[828, [1, 2, 3, 4, 6, 9, 12, 18, 23, 36, 46, 69, 92, 138, 207, 276, 414, 828]]
[829, [1, 829]]
[830, [1, 2, 5, 10, 83, 166, 415, 830]]
[831, [1, 3, 277, 831]]
[832, [1, 2, 4, 8, 13, 16, 26, 32, 52, 64, 104, 208, 416, 832]]
[833, [1, 7, 17, 49, 119, 833]]
[834, [1, 2, 3, 6, 139, 278, 417, 834]]
[835, [1, 5, 167, 835]]
[836, [1, 2, 4, 11, 19, 22, 38, 44, 76, 209, 418, 836]]
[837, [1, 3, 9, 27, 31, 93, 279, 837]]
[838, [1, 2, 419, 838]]
[839, [1, 839]]
[840, [1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, 840]]
[841, [1, 29, 841]]
[842, [1, 2, 421, 842]]
[843, [1, 3, 281, 843]]
[844, [1, 2, 4, 211, 422, 844]]
[845, [1, 5, 13, 65, 169, 845]]
[846, [1, 2, 3, 6, 9, 18, 47, 94, 141, 282, 423, 846]]
[847, [1, 7, 11, 77, 121, 847]]
[848, [1, 2, 4, 8, 16, 53, 106, 212, 424, 848]]
[849, [1, 3, 283, 849]]
[850, [1, 2, 5, 10, 17, 25, 34, 50, 85, 170, 425, 850]]
[851, [1, 23, 37, 851]]
[852, [1, 2, 3, 4, 6, 12, 71, 142, 213, 284, 426, 852]]
[853, [1, 853]]
[854, [1, 2, 7, 14, 61, 122, 427, 854]]
[855, [1, 3, 5, 9, 15, 19, 45, 57, 95, 171, 285, 855]]
[856, [1, 2, 4, 8, 107, 214, 428, 856]]
[857, [1, 857]]
[858, [1, 2, 3, 6, 11, 13, 22, 26, 33, 39, 66, 78, 143, 286, 429, 858]]
[859, [1, 859]]
[860, [1, 2, 4, 5, 10, 20, 43, 86, 172, 215, 430, 860]]
[861, [1, 3, 7, 21, 41, 123, 287, 861]]
[862, [1, 2, 431, 862]]
[863, [1, 863]]
[864, [1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 96, 108, 144, 216, 288, 432, 864]]
[865, [1, 5, 173, 865]]
[866, [1, 2, 433, 866]]
[867, [1, 3, 17, 51, 289, 867]]
[868, [1, 2, 4, 7, 14, 28, 31, 62, 124, 217, 434, 868]]
[869, [1, 11, 79, 869]]
[870, [1, 2, 3, 5, 6, 10, 15, 29, 30, 58, 87, 145, 174, 290, 435, 870]]
[871, [1, 13, 67, 871]]
[872, [1, 2, 4, 8, 109, 218, 436, 872]]
[873, [1, 3, 9, 97, 291, 873]]
[874, [1, 2, 19, 23, 38, 46, 437, 874]]
[875, [1, 5, 7, 25, 35, 125, 175, 875]]
[876, [1, 2, 3, 4, 6, 12, 73, 146, 219, 292, 438, 876]]
[877, [1, 877]]
[878, [1, 2, 439, 878]]
[879, [1, 3, 293, 879]]
[880, [1, 2, 4, 5, 8, 10, 11, 16, 20, 22, 40, 44, 55, 80, 88, 110, 176, 220, 440, 880]]
[881, [1, 881]]
[882, [1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 49, 63, 98, 126, 147, 294, 441, 882]]
[883, [1, 883]]
[884, [1, 2, 4, 13, 17, 26, 34, 52, 68, 221, 442, 884]]
[885, [1, 3, 5, 15, 59, 177, 295, 885]]
[886, [1, 2, 443, 886]]
[887, [1, 887]]
[888, [1, 2, 3, 4, 6, 8, 12, 24, 37, 74, 111, 148, 222, 296, 444, 888]]
[889, [1, 7, 127, 889]]
[890, [1, 2, 5, 10, 89, 178, 445, 890]]
[891, [1, 3, 9, 11, 27, 33, 81, 99, 297, 891]]
[892, [1, 2, 4, 223, 446, 892]]
[893, [1, 19, 47, 893]]
[894, [1, 2, 3, 6, 149, 298, 447, 894]]
[895, [1, 5, 179, 895]]
[896, [1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 128, 224, 448, 896]]
[897, [1, 3, 13, 23, 39, 69, 299, 897]]
[898, [1, 2, 449, 898]]
[899, [1, 29, 31, 899]]
[900, [1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 150, 180, 225, 300, 450, 900]]
[901, [1, 17, 53, 901]]
[902, [1, 2, 11, 22, 41, 82, 451, 902]]
[903, [1, 3, 7, 21, 43, 129, 301, 903]]
[904, [1, 2, 4, 8, 113, 226, 452, 904]]
[905, [1, 5, 181, 905]]
[906, [1, 2, 3, 6, 151, 302, 453, 906]]
[907, [1, 907]]
[908, [1, 2, 4, 227, 454, 908]]
[909, [1, 3, 9, 101, 303, 909]]
[910, [1, 2, 5, 7, 10, 13, 14, 26, 35, 65, 70, 91, 130, 182, 455, 910]]
[911, [1, 911]]
[912, [1, 2, 3, 4, 6, 8, 12, 16, 19, 24, 38, 48, 57, 76, 114, 152, 228, 304, 456, 912]]
[913, [1, 11, 83, 913]]
[914, [1, 2, 457, 914]]
[[915, [1, 3, 5, 15, 61, 183, 305, 915]]
[916, [1, 2, 4, 229, 458, 916]]
[917, [1, 7, 131, 917]]
[918, [1, 2, 3, 6, 9, 17, 18, 27, 34, 51, 54, 102, 153, 306, 459, 918]]
[919, [1, 919]]
[920, [1, 2, 4, 5, 8, 10, 20, 23, 40, 46, 92, 115, 184, 230, 460, 920]]
[921, [1, 3, 307, 921]]
[922, [1, 2, 461, 922]]
[923, [1, 13, 71, 923]]
[924, [1, 2, 3, 4, 6, 7, 11, 12, 14, 21, 22, 28, 33, 42, 44, 66, 77, 84, 132, 154, 231, 308, 462, 924]]
[925, [1, 5, 25, 37, 185, 925]]
[926, [1, 2, 463, 926]]
[927, [1, 3, 9, 103, 309, 927]]
[928, [1, 2, 4, 8, 16, 29, 32, 58, 116, 232, 464, 928]]
[929, [1, 929]]
[930, [1, 2, 3, 5, 6, 10, 15, 30, 31, 62, 93, 155, 186, 310, 465, 930]]
[931, [1, 7, 19, 49, 133, 931]]
[932, [1, 2, 4, 233, 466, 932]]
[933, [1, 3, 311, 933]]
[934, [1, 2, 467, 934]]
[935, [1, 5, 11, 17, 55, 85, 187, 935]]
[936, [1, 2, 3, 4, 6, 8, 9, 12, 13, 18, 24, 26, 36, 39, 52, 72, 78, 104, 117, 156, 234, 312, 468, 936]]
[937, [1, 937]]
[938, [1, 2, 7, 14, 67, 134, 469, 938]]
[939, [1, 3, 313, 939]]
[940, [1, 2, 4, 5, 10, 20, 47, 94, 188, 235, 470, 940]]
[941, [1, 941]]
[942, [1, 2, 3, 6, 157, 314, 471, 942]]
[943, [1, 23, 41, 943]]
[944, [1, 2, 4, 8, 16, 59, 118, 236, 472, 944]]
[945, [1, 3, 5, 7, 9, 15, 21, 27, 35, 45, 63, 105, 135, 189, 315, 945]]
[946, [1, 2, 11, 22, 43, 86, 473, 946]]
[947, [1, 947]]
[948, [1, 2, 3, 4, 6, 12, 79, 158, 237, 316, 474, 948]]
[949, [1, 13, 73, 949]]
[950, [1, 2, 5, 10, 19, 25, 38, 50, 95, 190, 475, 950]]
[951, [1, 3, 317, 951]]
[952, [1, 2, 4, 7, 8, 14, 17, 28, 34, 56, 68, 119, 136, 238, 476, 952]]
[953, [1, 953]]
[954, [1, 2, 3, 6, 9, 18, 53, 106, 159, 318, 477, 954]]
[955, [1, 5, 191, 955]]
[956, [1, 2, 4, 239, 478, 956]]
[957, [1, 3, 11, 29, 33, 87, 319, 957]]
[958, [1, 2, 479, 958]]
[959, [1, 7, 137, 959]]
[960, [1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480, 960]]
[961, [1, 31, 961]]
[962, [1, 2, 13, 26, 37, 74, 481, 962]]
[963, [1, 3, 9, 107, 321, 963]]
[964, [1, 2, 4, 241, 482, 964]]
[965, [1, 5, 193, 965]]
[966, [1, 2, 3, 6, 7, 14, 21, 23, 42, 46, 69, 138, 161, 322, 483, 966]]
[967, [1, 967]]
[968, [1, 2, 4, 8, 11, 22, 44, 88, 121, 242, 484, 968]]
[969, [1, 3, 17, 19, 51, 57, 323, 969]]
[970, [1, 2, 5, 10, 97, 194, 485, 970]]
[971, [1, 971]]
[972, [1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, 972]]
[973, [1, 7, 139, 973]]
[974, [1, 2, 487, 974]]
[975, [1, 3, 5, 13, 15, 25, 39, 65, 75, 195, 325, 975]]
[976, [1, 2, 4, 8, 16, 61, 122, 244, 488, 976]]
[977, [1, 977]]
[978, [1, 2, 3, 6, 163, 326, 489, 978]]
[979, [1, 11, 89, 979]]
[980, [1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 49, 70, 98, 140, 196, 245, 490, 980]]
[981, [1, 3, 9, 109, 327, 981]]
[982, [1, 2, 491, 982]]
[983, [1, 983]]
[984, [1, 2, 3, 4, 6, 8, 12, 24, 41, 82, 123, 164, 246, 328, 492, 984]]
[985, [1, 5, 197, 985]]
[986, [1, 2, 17, 29, 34, 58, 493, 986]]
[987, [1, 3, 7, 21, 47, 141, 329, 987]]
[988, [1, 2, 4, 13, 19, 26, 38, 52, 76, 247, 494, 988]]
[989, [1, 23, 43, 989]]
[990, [1, 2, 3, 5, 6, 9, 10, 11, 15, 18, 22, 30, 33, 45, 55, 66, 90, 99, 110, 165, 198, 330, 495, 990]]
[991, [1, 991]]
[992, [1, 2, 4, 8, 16, 31, 32, 62, 124, 248, 496, 992]]
[993, [1, 3, 331, 993]]
[994, [1, 2, 7, 14, 71, 142, 497, 994]]
[995, [1, 5, 199, 995]]
[996, [1, 2, 3, 4, 6, 12, 83, 166, 249, 332, 498, 996]]
[997, [1, 997]]
[998, [1, 2, 499, 998]]
[999, [1, 3, 9, 27, 37, 111, 333, 999]]
[1000, [1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000]]]
Теперь несложно посчитать и сумму делителей чисел от 1 до 1000(которые тоже были получены с помощью программы Derive (по формуле 2.), теперь делители «a» просто складывались):
[1, 1]
[2, 3]
[3, 4]
[4, 7]
[5, 6]
[6, 12]
[7, 8]
[8, 15]
[9, 13]
[10, 18]
[11, 12]
[12, 28]
[13, 14]
[14, 24]
[15, 24]
[16, 31]
[17, 18]
[18, 39]
[19, 20]
[20, 42]
[21, 32]
[22, 36]
[23, 24]
[24, 60]
[25, 31]
[26, 42]
[27, 40]
[28, 56]
[29, 30]
[30, 72]
[31, 32]
[32, 63]
[33, 48]
[34, 54]
[35, 48]
[36, 91]
[37, 38]
[38, 60]
[39, 56]
[40, 90]
[41, 42]
[42, 96]
[43, 44]
[44, 84]
[45, 78]
[46, 72]
[47, 48]
[48, 124]
[49, 57]
[50, 93]
[51, 72]
[52, 98]
[53, 54]
[54, 120]
[55, 72]
[56, 120]
[57, 80]
[58, 90]
[59, 60]
[60, 168]
[61, 62]
[62, 96]
[63, 104]
[64, 127]
[65, 84]
[66, 144]
[67, 68]
[68, 126]
[69, 96]
[70, 144]
[71, 72]
[72, 195]
[73, 74]
[74, 114]
[75, 124]
[76, 140]
[77, 96]
[78, 168]
[79, 80]
[80, 186]
[81, 121]
[82, 126]
[83, 84]
[84, 224]
[85, 108]
[86, 132]
[87, 120]
[88, 180]
[89, 90]
[90, 234]
[91, 112]
[92, 168]
[93, 128]
[94, 144]
[95, 120]
[96, 252]
[97, 98]
[98, 171]
[99, 156]
[100, 217]
[101, 102]
[102, 216]
[103, 104]
[104, 210]
[105, 192]
[106, 162]
[107, 108]
[108, 280]
[109, 110]
[110, 216]
[111, 152]
[112, 248]
[113, 114]
[114, 240]
[115, 144]
[116, 210]
[117, 182]
[118, 180]
[119, 144]
[120, 360]
[121, 133]
[122, 186]
[123, 168]
[124, 224]
[125, 156]
[126, 312]
[127, 128]
[128, 255]
[129, 176]
[130, 252]
[131, 132]
[132, 336]
[133, 160]
[134, 204]
[135, 240]
[136, 270]
[137, 138]
[138, 288]
[139, 140]
[140, 336]
[141, 192]
[142, 216]
[143, 168]
[144, 403]
[145, 180]
[146, 222]
[147, 228]
[148, 266]
[149, 150]
[150, 372]
[151, 152]
[152, 300]
[153, 234]
[154, 288]
[155, 192]
[156, 392]
[157, 158]
[158, 240]
[159, 216]
[160, 378]
[161, 192]
[162, 363]
[163, 164]
[164, 294]
[165, 288]
[166, 252]
[167, 168]
[168, 480]
[169, 183]
[170, 324]
[171, 260]
[172, 308]
[173, 174]
[174, 360]
[175, 248]
[176, 372]
[177, 240]
[178, 270]
[179, 180]
[180, 546]
[181, 182]
[182, 336]
[183, 248]
[184, 360]
[185, 228]
[186, 384]
[187, 216]
[188, 336]
[189, 320]
[190, 360]
[191, 192]
[192, 508]
[193, 194]
[194, 294]
[195, 336]
[196, 399]
[197, 198]
[198, 468]
[199, 200]
[200, 465]
[201, 272]
[202, 306]
[203, 240]
[204, 504]
[205, 252]
[206, 312]
[207, 312]
[208, 434]
[209, 240]
[210, 576]
[211, 212]
[212, 378]
[213, 288]
[214, 324]
[215, 264]
[216, 600]
[217, 256]
[218, 330]
[219, 296]
[220, 504]
[221, 252]
[222, 456]
[223, 224]
[224, 504]
[225, 403]
[226, 342]
[227, 228]
[228, 560]
[229, 230]
[230, 432]
[231, 384]
[232, 450]
[233, 234]
[234, 546]
[235, 288]
[236, 420]
[237, 320]
[238, 432]
[239, 240]
[240, 744]
[241, 242]
[242, 399]
[243, 364]
[244, 434]
[245, 342]
[246, 504]
[247, 280]
[248, 480]
[249, 336]
[250, 468]
[251, 252]
[252, 728]
[253, 288]
[254, 384]
[255, 432]
[256, 511]
[257, 258]
[258, 528]
[259, 304]
[260, 588]
[261, 390]
[262, 396]
[263, 264]
[264, 720]
[265, 324]
[266, 480]
[267, 360]
[268, 476]
[269, 270]
[270, 720]
[271, 272]
[272, 558]
[273, 448]
[274, 414]
[275, 372]
[276, 672]
[277, 278]
[278, 420]
[279, 416]
[280, 720]
[281, 282]
[282, 576]
[283, 284]
[284, 504]
[285, 480]
[286, 504]
[287, 336]
[288, 819]
[289, 307]
[290, 540]
[291, 392]
[292, 518]
[293, 294]
[294, 684]
[295, 360]
[296, 570]
[297, 480]
[298, 450]
[299, 336]
[300, 868]
[301, 352]
[302, 456]
[303, 408]
[304, 620]
[305, 372]
[306, 702]
[307, 308]
[308, 672]
[309, 416]
[310, 576]
[311, 312]
[312, 840]
[313, 314]
[314, 474]
[315, 624]
[316, 560]
[317, 318]
[318, 648]
[319, 360]
[320, 762]
[321, 432]
[322, 576]
[323, 360]
[324, 847]
[325, 434]
[326, 492]
[327, 440]
[328, 630]
[329, 384]
[330, 864]
[331, 332]
[332, 588]
[333, 494]
[334, 504]
[335, 408]
[336, 992]
[337, 338]
[338, 549]
[339, 456]
[340, 756]
[341, 384]
[342, 780]
[343, 400]
[344, 660]
[345, 576]
[346, 522]
[347, 348]
[348, 840]
[349, 350]
[350, 744]
[351, 560]
[352, 756]
[353, 354]
[354, 720]
[355, 432]
[356, 630]
[357, 576]
[358, 540]
[359, 360]
[360, 1170]
[361, 381]
[362, 546]
[363, 532]
[364, 784]
[365, 444]
[366, 744]
[367, 368]
[368, 744]
[369, 546]
[370, 684]
[371, 432]
[372, 896]
[373, 374]
[374, 648]
[375, 624]
[376, 720]
[377, 420]
[378, 960]
[379, 380]
[380, 840]
[381, 512]
[382, 576]
[383, 384]
[384, 1020]
[385, 576]
[386, 582]
[387, 572]
[388, 686]
[389, 390]
[390, 1008]
[391, 432]
[392, 855]
[393, 528]
[394, 594]
[395, 480]
[396, 1092]
[397, 398]
[398, 600]
[399, 640]
[400, 961]
[401, 402]
[402, 816]
[403, 448]
[404, 714]
[405, 726]
[406, 720]
[407, 456]
[408, 1080]
[409, 410]
[410, 756]
[411, 552]
[412, 728]