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Сумма делителей числа (стр. 4 из 5)

[603, 884]

[604, 1064]

[605, 798]

[606, 1224]

[607, 608]

[608, 1260]

[609, 960]

[610, 1116]

[611, 672]

[612, 1638]

[613, 614]

[614, 924]

[615, 1008]

[616, 1440]

[617, 618]

[618, 1248]

[619, 620]

[620, 1344]

[621, 960]

[622, 936]

[623, 720]

[624, 1736]

[625, 781]

[626, 942]

[627, 960]

[628, 1106]

[629, 684]

[630, 1872]

[631, 632]

[632, 1200]

[633, 848]

[634, 954]

[635, 768]

[636, 1512]

[637, 798]

[638, 1080]

[639, 936]

[640, 1530]

[641, 642]

[642, 1296]

[643, 644]

[644, 1344]

[645, 1056]

[646, 1080]

[647, 648]

[648, 1815]

[649, 720]

[650, 1302]

[651, 1024]

[652, 1148]

[653, 654]

[654, 1320]

[655, 792]

[656, 1302]

[657, 962]

[658, 1152]

[659, 660]

[660, 2016]

[661, 662]

[662, 996]

[663, 1008]

[664, 1260]

[665, 960]

[666, 1482]

[667, 720]

[668, 1176]

[669, 896]

[670, 1224]

[671, 744]

[672, 2016]

[673, 674]

[674, 1014]

[675, 1240]

[676, 1281]

[677, 678]

[678, 1368]

[679, 784]

[680, 1620]

[681, 912]

[682, 1152]

[683, 684]

[684, 1820]

[685, 828]

[686, 1200]

[687, 920]

[688, 1364]

[689, 756]

[690, 1728]

[691, 692]

[692, 1218]

[693, 1248]

[694, 1044]

[695, 840]

[696, 1800]

[697, 756]

[698, 1050]

[699, 936]

[700, 1736]

[701, 702]

[702, 1680]

[703, 760]

[704, 1524]

[705, 1152]

[706, 1062]

[707, 816]

[708, 1680]

[709, 710]

[710, 1296]

[711, 1040]

[712, 1350]

[713, 768]

[714, 1728]

[715, 1008]

[716, 1260]

[717, 960]

[718, 1080]

[719, 720]

[720, 2418]

[721, 832]

[722, 1143]

[723, 968]

[724, 1274]

[725, 930]

[726, 1596]

[727, 728]

[728, 1680]

[729, 1093]

[730, 1332]

[731, 792]

[732, 1736]

[733, 734]

[734, 1104]

[735, 1368]

[736, 1512]

[737, 816]

[738, 1638]

[739, 740]

[740, 1596]

[741, 1120]

[742, 1296]

[743, 744]

[744, 1920]

[745, 900]

[746, 1122]

[747, 1092]

[748, 1512]

[749, 864]

[750, 1872]

[751, 752]

[752, 1488]

[753, 1008]

[754, 1260]

[755, 912]

[756, 2240]

[757, 758]

[758, 1140]

[759, 1152]

[760, 1800]

[761, 762]

[762, 1536]

[763, 880]

[764, 1344]

[765, 1404]

[766, 1152]

[767, 840]

[768, 2044]

[769, 770]

[770, 1728]

[771, 1032]

[772, 1358]

[773, 774]

[774, 1716]

[775, 992]

[776, 1470]

[777, 1216]

[778, 1170]

[779, 840]

[780, 2352]

[781, 864]

[782, 1296]

[783, 1200]

[784, 1767]

[785, 948]

[786, 1584]

[787, 788]

[788, 1386]

[789, 1056]

[790, 1440]

[791, 912]

[792, 2340]

[793, 868]

[794, 1194]

[795, 1296]

[796, 1400]

[797, 798]

[798, 1920]

[799, 864]

[800, 1953]

[801, 1170]

[802, 1206]

[803, 888]

[804, 1904]


[805, 1152]

[806, 1344]

[807, 1080]

[808, 1530]

[809, 810]

[810, 2178]

[811, 812]

[812, 1680]

[813, 1088]

[814, 1368]

[815, 984]

[816, 2232]

[817, 880]

[818, 1230]

[819, 1456]

[820, 1764]

[821, 822]

[822, 1656]

[823, 824]

[824, 1560]

[825, 1488]

[826, 1440]

[827, 828]

[828, 2184]

[829, 830]

[830, 1512]

[831, 1112]

[832, 1778]

[833, 1026]

[834, 1680]

[835, 1008]

[836, 1680]

[837, 1280]

[838, 1260]

[839, 840]

[840, 2880]

[841, 871]

[842, 1266]

[843, 1128]

[844, 1484]

[845, 1098]

[846, 1872]

[847, 1064]

[848, 1674]

[849, 1136]

[850, 1674]

[851, 912]

[852, 2016]

[853, 854]

[854, 1488]

[855, 1560]

[856, 1620]

[857, 858]

[858, 2016]

[859, 860]

[860, 1848]

[861, 1344]

[862, 1296]

[863, 864]

[864, 2520]

[865, 1044]

[866, 1302]

[867, 1228]

[868, 1792]

[869, 960]

[870, 2160]

[871, 952]

[872, 1650]

[873, 1274]

[874, 1440]

[875, 1248]

[876, 2072]

[877, 878]

[878, 1320]

[879, 1176]

[880, 2232]

[881, 882]

[882, 2223]

[883, 884]

[884, 1764]

[885, 1440]

[886, 1332]

[887, 888]

[888, 2280]

[889, 1024]

[890, 1620]

[891, 1452]

[892, 1568]

[893, 960]

[894, 1800]

[895, 1080]

[896, 2040]

[897, 1344]

[898, 1350]

[899, 960]

[900, 2821]

[901, 972]

[902, 1512]

[903, 1408]

[904, 1710]

[905, 1092]

[906, 1824]

[907, 908]

[908, 1596]

[909, 1326]

[910, 2016]

[911, 912]

[912, 2480]

[913, 1008]

[914, 1374]

[915, 1488]

[916, 1610]

[917, 1056]

[918, 2160]

[919, 920]

[920, 2160]

[921, 1232]

[922, 1386]

[923, 1008]

[924, 2688]

[925, 1178]

[926, 1392]

[927, 1352]

[928, 1890]

[929, 930]

[930, 2304]

[931, 1140]

[932, 1638]

[933, 1248]

[934, 1404]

[935, 1296]

[936, 2730]

[937, 938]

[938, 1632]

[939, 1256]

[940, 2016]

[941, 942]

[942, 1896]

[943, 1008]

[944, 1860]

[945, 1920]

[946, 1584]

[947, 948]

[948, 2240]

[949, 1036]

[950, 1860]

[951, 1272]

[952, 2160]

[953, 954]

[954, 2106]

[955, 1152]

[956, 1680]

[957, 1440]

[958, 1440]

[959, 1104]

[960, 3048]

[961, 993]

[962, 1596]

[963, 1404]

[964, 1694]

[965, 1164]

[966, 2304]

[967, 968]

[968, 1995]

[969, 1440]

[970, 1764]

[971, 972]

[972, 2548]

[973, 1120]

[974, 1464]

[975, 1736]

[976, 1922]

[977, 978]

[978, 1968]

[979, 1080]

[980, 2394]

[981, 1430]

[982, 1476]

[983, 984]

[984, 2520]

[985, 1188]

[986, 1620]

[987, 1536]

[988, 1960]

[989, 1056]

[990, 2808]

[991, 992]

[992, 2016]

[993, 1328]

[994, 1728]

[995, 1200]

[996, 2352]

[997, 998]

[998, 1500]

[999, 1520]

[1000, 2340]


Теперь посмотрим, все ли числа являются суммой делителей какого-либо числа и есть ли такие числа сумма делителей которых равна (в первых двух сотнях).

Ниже приведена таблица: [[4, 7]](на втором месте сумма делителей, а на первом число с данной суммой делителей) … [[1, 1]], [2] (т.е. нет такого числа с суммой делителей равной двум):


[1,1]

[2]

[2,3]

[3,4]

[5]

[5,6]

[4,7]

[7,8]

[9]

[10]

[11]

[6,12]

[11, 12]

[9,13]

[13,14]

[8,15]

[16]

[17]

[10,18]

[17,18]

[19]

[19.20]

[21]

[22]

[23]

[14,24]

[15,24]

[23,24]

[25]

[26]

[27]

[12, 28].

[29]

[29,30]

[16,31]

[25.31]

[21,32]

[31,32]

[33]

[34]

[35]

[22,36]

[37]

[37,38]

[18,39]

[27, 40]

[41]

[20,42]

[26,42]

[41,42].

[43]

[43,44].

[45]

[46]

[47]

[33,48].

[35,4 8]

[47,48]

[49]

[50]

[51]

[52]

[53]

[34,54]

[53, 54]

[55]

[28,56]

[39.56]

[49,57]

[58]

[59]

[24,60]

[38.60]

[59,60]

[61]

[61,62]

[32,63]

[64]

[65]

[66]

[67]

[67, 68]

[69]

[70]

[71]

[30,72]

[46,72]

[51,72]

[55,72]

[71,72]

[73]

[73,74]

[75]

[76]

[77]

[45,78]

[79]

[57,80]

[79,80]

[81]

[82]

[83]

[44,84]

[65,84]

[83,84]

[85]

[86]

[87]

[88]

[89]

[40, 90]

[58,90]

[89,90]

[36,91]

[92]

[50,93].

[94]

[95]

[42, 96]

[62,96]

[69,96]

[77,96]

[97]

[52,98]

[97,98]

[99]

[100]

[101]

[102]

[103]

[63,104]

[105]

[106]

[107]

[85,108]

[109]

[110]

[111]

[91, 112]

[113]

[74,114],

[115]

[116]

[117]

[118]

[119]

[54,120]

[56,120]

[87,120]

[95,120]

[81,121]

[122]

[123]

[48,124]

[75, 124]

[125]

[68,126]

[82.126]

[64,127]

[9 3,128]

[129]

[130]

[131]

[86,132]

[133]

[134]

[135]

[136]

[137]

[138]

[139]

[76,140]

[141]

[142]

[143]

[66,144]

[70,144]

[94,144]

[145]

[146]

[147]

[178]

[149]

[150]

[151]

[152]

[153]

[154]

[155]

[99,156]

[157]

[158]

[159]

[160]

[161]

[162]

[163]

[164]

[165]

[166]

[167]

[60,168]

[78,168]

[92,168]

[169]

[170]

[98,171]

[172]

[173]

[174]

[175]

[176]

[177]

[178]

[179]

[88,180]

[181]

[182]

[183]

[184]

[185]

[80,186]

[187]

[188]

[189]

[190]

[191]

[192]

[193]

[194]

[72,195]

[196]

[197]

[198]

[199]

[200]


Как мы заметили, есть такие числа, которые не являются суммой делителей ни одного числа и так же есть такие числа, которые являются суммой делителей ни одного, а нескольких чисел. Теперь посмотрим только те числа, которые являются суммой делителей ни одного, а нескольких чисел:


[6,12], [11,12]

[10,18], [17,18]

[14,24], [15,24], [23,24]