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Incompleti (numeri)

Rappresentazione dei numeri 

Si chiamano “incompleti” i numeri naturali n tali nessun intero è n volte la somma delle proprie cifre.

 

Solo alcuni interi sono un multiplo della somma delle proprie cifre; per esempio, 11 non è multiplo di 2, né 15 di 6. In particolare i numeri primi rappresentati con due o più cifre non possono essere un multiplo della somma delle loro cifre.

Invece 18 è il doppio della somma, 9, e 24 il quadruplo, ma nessun numero è 63 volte la somma delle proprie cifre.

 

Qui trovate i primi 10000 numeri incompleti in base 10 (N.J.A. Sloane e Mira Bernstein, The Online Encyclopedia of Integer Sequences http://oeis.org).

 

La definizione dipende dalla base della rappresentazione; la tabella seguente riporta i numeri incompleti fino a 1000 nelle basi sino a 20.

Base

Numeri incompleti fino a 1000

2

13, 19, 25, 26, 35, 38, 47, 49, 50, 52, 55, 67, 70, 76, 94, 95, 97, 98, 100, 103, 104, 109, 110, 115, 117, 131, 134, 140, 151, 152, 157, 159, 171, 175, 179, 183, 185, 187, 188, 190, 193, 194, 196, 199, 200, 203, 206, 208, 217, 218, 220, 227, 229, 230, 234, 249, 253, 259, 262, 268, 279, 280, 283, 287, 295, 299, 302, 304, 309, 313, 314, 318, 319, 327, 333, 335, 341, 342, 345, 350, 351, 358, 366, 367, 369, 370, 371, 373, 374, 375, 376, 380, 385, 386, 388, 391, 392, 398, 400, 405, 406, 407, 411, 412, 416, 423, 429, 433, 434, 435, 436, 440, 443, 451, 453, 454, 457, 458, 459, 460, 467, 468, 471, 475, 485, 489, 491, 497, 498, 501, 505, 506, 515, 518, 524, 535, 536, 539, 543, 555, 558, 560, 566, 569, 573, 574, 575, 590, 591, 595, 598, 599, 604, 607, 608, 613, 618, 621, 626, 627, 628, 631, 636, 638, 647, 654, 659, 666, 670, 679, 682, 684, 685, 687, 689, 690, 695, 700, 702, 716, 729, 731, 732, 734, 737, 738, 739, 740, 742, 745, 746, 748, 750, 752, 760, 761, 769, 770, 772, 775, 776, 782, 784, 791, 795, 796, 797, 799, 800, 805, 809, 810, 812, 814, 822, 824, 829, 832, 841, 846, 857, 858, 859, 865, 866, 867, 868, 869, 870, 872, 875, 880, 886, 899, 901, 902, 906, 908, 913, 914, 915, 916, 917, 918, 920, 921, 931, 933, 934, 936, 937, 939, 942, 950, 969, 970, 973, 977, 978, 981, 982, 985, 993, 994, 996

3

17, 32, 44, 51, 94, 95, 96, 106, 107, 112, 118, 132, 148, 153, 199, 224, 226, 232, 235, 236, 238, 256, 265, 268, 269, 274, 277, 281, 282, 284, 285, 288, 296, 308, 318, 321, 334, 336, 343, 352, 354, 368, 396, 442, 443, 444, 454, 459, 469, 472, 478, 511, 512, 538, 584, 586, 595, 597, 607, 616, 632, 638, 658, 664, 667, 672, 676, 677, 678, 685, 686, 688, 694, 696, 698, 703, 705, 706, 708, 712, 714, 716, 724, 742, 751, 754, 755, 766, 767, 768, 778, 781, 794, 795, 802, 804, 805, 806, 807, 808, 814, 818, 822, 826, 827, 831, 832, 842, 843, 846, 851, 852, 855, 864, 871, 872, 874, 880, 888, 901, 911, 913, 923, 924, 928, 937, 940, 944, 952, 954, 958, 963, 964, 982, 988, 991, 995, 1000

4

29, 41, 71, 83, 93, 111, 113, 114, 116, 117, 122, 123, 125, 135, 137, 143, 146, 153, 164, 167, 191, 197, 201, 237, 242, 263, 275, 279, 282, 284, 285, 291, 303, 305, 311, 323, 326, 327, 332, 359, 362, 369, 372, 375, 377, 382, 383, 389, 407, 410, 411, 414, 415, 417, 419, 422, 423, 431, 435, 437, 443, 444, 446, 447, 449, 450, 452, 453, 456, 458, 459, 461, 464, 468, 483, 486, 488, 491, 492, 498, 500, 503, 519, 521, 531, 539, 540, 548, 551, 561, 563, 567, 572, 578, 584, 605, 611, 612, 615, 623, 626, 647, 651, 656, 663, 668, 711, 713, 723, 735, 743, 753, 755, 759, 764, 773, 783, 785, 786, 788, 791, 794, 795, 803, 804, 807, 815, 819, 843, 863, 879, 891, 941, 948, 963, 966, 968, 983, 987

5

16, 22, 28, 46, 56, 58, 68, 74, 76, 80, 106, 108, 110, 118, 128, 136, 138, 140, 146, 152, 168, 198, 202, 206, 208, 230, 249, 256, 258, 262, 263, 268, 274, 276, 278, 280, 284, 286, 288, 290, 292, 294, 296, 298, 302, 318, 323, 324, 326, 336, 338, 340, 346, 352, 354, 362, 366, 368, 370, 376, 380, 386, 400, 406, 418, 448, 452, 456, 458, 462, 466, 508, 512, 518, 524, 526, 530, 536, 540, 550, 578, 584, 586, 588, 590, 596, 598, 602, 604, 612, 622, 628, 636, 638, 640, 646, 652, 664, 666, 674, 676, 680, 688, 690, 700, 706, 708, 712, 716, 730, 752, 758, 760, 764, 766, 778, 796, 836, 838, 840, 846, 852, 886, 898, 902, 914, 916, 934, 964, 968, 974, 976, 978, 982, 984, 986, 988, 990

6

27, 33, 64, 82, 97, 100, 103, 104, 107, 118, 122, 124, 125, 128, 134, 135, 152, 159, 162, 177, 190, 193, 195, 198, 205, 208, 212, 214, 232, 233, 250, 277, 280, 298, 334, 343, 345, 349, 352, 358, 362, 363, 364, 370, 380, 382, 384, 403, 427, 442, 448, 449, 452, 464, 475, 478, 487, 489, 490, 492, 499, 503, 513, 515, 517, 529, 532, 535, 538, 539, 550, 553, 554, 557, 560, 565, 568, 574, 577, 578, 579, 580, 582, 592, 593, 598, 600, 607, 608, 610, 613, 614, 615, 617, 618, 620, 623, 624, 625, 628, 629, 632, 634, 638, 639, 640, 642, 658, 664, 665, 668, 682, 694, 697, 704, 708, 718, 722, 723, 724, 725, 728, 730, 732, 737, 740, 742, 744, 749, 750, 768, 782, 783, 800, 804, 807, 810, 835, 838, 859, 863, 874, 880, 884, 898, 908, 912, 943, 949, 954, 972, 979, 982, 993

7

30, 86, 102, 134, 138, 141, 158, 162, 167, 170, 183, 186, 194, 210, 213, 233, 284, 290, 306, 312, 314, 326, 330, 338, 354, 362, 366, 368, 428, 452, 480, 530, 534, 536, 540, 542, 554, 564, 578, 591, 602, 645, 648, 656, 705, 708, 714, 740, 746, 761, 762, 789, 792, 794, 828, 852, 876, 890, 894, 906, 908, 909, 911, 914, 929, 930, 932, 933, 935, 936, 938, 942, 947, 951, 954, 956, 957, 960, 962, 966, 968, 974, 978, 983, 987, 992, 993

8

42, 44, 51, 52, 60, 105, 109, 116, 124, 173, 177, 178, 181, 201, 205, 209, 210, 213, 214, 217, 233, 237, 241, 242, 245, 249, 250, 251, 254, 255, 269, 273, 277, 278, 282, 285, 287, 290, 298, 299, 300, 308, 336, 343, 348, 352, 397, 401, 402, 403, 404, 408, 412, 416, 425, 429, 433, 434, 437, 444, 461, 465, 466, 469, 473, 474, 476, 480, 489, 493, 497, 501, 506, 509, 525, 537, 538, 541, 543, 546, 562, 565, 570, 573, 579, 621, 628, 636, 653, 685, 689, 690, 693, 717, 762, 765, 777, 781, 786, 789, 790, 793, 794, 797, 802, 809, 817, 818, 821, 826, 829, 830, 831, 833, 836, 837, 839, 840, 845, 854, 858, 861, 863, 866, 872, 884, 909, 928, 950, 977, 978, 982, 986, 992

9

46, 47, 48, 56, 58, 66, 76, 86, 136, 138, 167, 176, 222, 227, 228, 248, 258, 298, 302, 308, 312, 316, 318, 338, 343, 344, 347, 348, 352, 354, 356, 358, 362, 374, 383, 384, 392, 398, 402, 403, 404, 406, 407, 408, 411, 412, 414, 416, 422, 423, 426, 432, 436, 462, 491, 500, 504, 522, 552, 562, 572, 582, 586, 590, 594, 598, 622, 626, 632, 636, 662, 672, 676, 678, 680, 682, 684, 707, 708, 716, 726, 734, 744, 762, 764, 767, 768, 770, 774, 794, 798, 804, 860, 866, 868, 876, 886, 896, 906, 946, 950, 956, 986, 996

10

62, 63, 65, 75, 84, 95, 161, 173, 195, 216, 261, 266, 272, 276, 326, 371, 372, 377, 381, 383, 386, 387, 395, 411, 416, 422, 426, 431, 432, 438, 441, 443, 461, 466, 471, 476, 482, 483, 486, 488, 491, 492, 493, 494, 497, 498, 516, 521, 522, 527, 531, 533, 536, 542, 543, 546, 549, 552, 553, 563, 564, 573, 575, 612, 615, 620, 623, 630, 635, 639, 645, 650, 675, 716, 723, 750, 761, 771, 776, 785, 795, 816, 821, 822, 827, 831, 834, 839, 840, 845, 861, 866, 872, 876, 882, 926, 927, 932, 933, 936, 938, 941, 942, 945, 950, 966, 971, 972, 983, 986, 993

11

68, 70, 79, 80, 82, 92, 104, 200, 202, 212, 214, 224, 225, 248, 260, 314, 320, 332, 380, 392, 452, 458, 464, 490, 502, 508, 512, 513, 514, 518, 520, 524, 530, 562, 568, 574, 578, 579, 580, 584, 585, 590, 592, 595, 598, 599, 622, 628, 634, 635, 640, 644, 645, 650, 652, 658, 659, 662, 683, 688, 694, 695, 699, 700, 707, 710, 712, 717, 718, 722, 723, 724, 728, 740, 747, 748, 758, 763, 764, 770, 775, 805, 808, 853, 864, 868, 869, 872, 880, 890, 902, 938, 940, 980, 992, 998, 1000

12

86, 87, 88, 90, 99, 101, 102, 112, 113, 114, 125, 126, 138, 229, 235, 244, 245, 246, 256, 258, 269, 270, 282, 307, 373, 379, 385, 391, 392, 400, 402, 426, 451, 464, 530, 535, 536, 542, 543, 547, 548, 607, 608, 620, 667, 673, 674, 679, 680, 685, 686, 687, 691, 692, 693, 697, 698, 699, 700, 703, 704, 706, 714, 739, 745, 746, 751, 752, 757, 758, 759, 763, 764, 765, 769, 770, 772, 775, 776, 777, 778, 783, 784, 805, 811, 817, 818, 823, 824, 830, 831, 835, 836, 841, 842, 843, 844, 847, 849, 850, 853, 854, 855, 856, 857, 860, 861, 862, 863, 883, 895, 896, 901, 902, 907, 908, 909, 913, 915, 916, 919, 920, 921, 922, 926, 927, 928, 931, 932, 934, 935, 939, 940, 950, 951, 952, 953, 954, 963, 964, 965, 966, 976, 978

13

92, 96, 108, 110, 120, 134, 162, 176, 276, 278, 290, 318, 450, 456, 458, 459, 500, 514, 528, 540, 612, 618, 626, 632, 640, 683, 696, 710, 794, 800, 807, 816, 822, 824, 852, 866, 872, 878, 891, 894, 900, 908, 912, 914, 950, 956, 957, 963, 978, 984, 990, 992, 995, 996, 998

14

114, 115, 116, 117, 119, 129, 130, 132, 133, 145, 146, 147, 159, 160, 161, 174, 175, 189, 309, 316, 325, 327, 328, 329, 340, 342, 343, 355, 356, 357, 370, 371, 385, 414, 505, 512, 519, 520, 526, 527, 536, 538, 539, 553, 566, 567, 581, 610, 624, 708, 715, 722, 723, 730, 731, 736, 737, 749, 777, 806, 821, 835, 918, 919, 925, 926, 927, 932, 933, 940, 941, 942, 946, 947, 995

15

122, 124, 126, 137, 138, 139, 140, 142, 154, 156, 157, 170, 172, 186, 202, 362, 364, 366, 378, 380, 382, 394, 410, 412, 426, 427, 458, 474, 578, 586, 594, 602, 604, 606, 607, 619, 620, 622, 698, 714, 818, 826, 842, 844, 860, 892, 908, 924, 938, 940, 954

16

147, 149, 150, 152, 163, 164, 165, 167, 168, 180, 183, 197, 198, 200, 215, 248, 419, 420, 422, 423, 437, 440, 453, 470, 488, 504, 537, 657, 665, 674, 692, 693, 695, 743, 744, 809, 810, 929, 930, 938, 945, 947, 953, 954, 965, 968

17

154, 155, 156, 158, 160, 172, 174, 176, 178, 190, 191, 192, 194, 208, 210, 212, 226, 228, 244, 246, 262, 280, 298, 460, 462, 464, 466, 480, 482, 484, 498, 500, 516, 518, 534, 551, 552, 587, 604, 740, 758, 766, 767, 768, 770, 772, 786, 790, 804, 822, 824, 840, 858, 876, 894, 910, 912

18

182, 183, 184, 185, 186, 187, 189, 201, 202, 203, 204, 206, 207, 220, 221, 223, 224, 225, 240, 241, 242, 243, 258, 259, 260, 261, 277, 278, 279, 296, 297, 315, 505, 514, 525, 526, 527, 529, 530, 531, 544, 546, 547, 548, 549, 563, 564, 566, 567, 582, 583, 584, 585, 601, 602, 603, 620, 621, 639, 676, 829, 838, 847, 848, 856, 857, 869, 870, 871, 872, 873, 887, 888, 890, 891, 906, 909, 925, 926, 927, 944, 945, 963, 1000

19

192, 194, 197, 198, 212, 213, 216, 218, 234, 236, 237, 251, 252, 272, 294, 312, 332, 572, 576, 578, 594, 596, 612, 614, 632, 636, 653, 654, 672, 674, 692, 693, 732, 752, 932, 942, 954, 956, 957, 959, 974, 975, 978

20

222, 223, 224, 225, 226, 227, 228, 230, 243, 244, 245, 246, 247, 249, 250, 264, 265, 266, 268, 269, 270, 285, 287, 288, 289, 290, 306, 307, 308, 309, 310, 327, 328, 329, 330, 348, 349, 350, 369, 370, 390, 621, 631, 643, 644, 645, 646, 648, 649, 650, 664, 665, 667, 668, 669, 670, 686, 688, 689, 690, 706, 707, 708, 709, 710, 727, 728, 729, 730, 748, 749, 750, 769, 770, 790, 831

 

La tabella seguente mostra il minimo intero uguale a n volte la somma delle cifre, per n da 1 a 20.

n

Minimo intero

1

1

2

18

3

27

4

12

5

45

6

54

7

21

8

72

9

81

10

10

11

198

12

108

13

117

14

126

15

135

16

144

17

153

18

162

19

114

20

180

 

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