Arithmetic Numbers

Arithmetic Numbers [OEIS::A003601] are numbers whose average of their divisors are integers. Note: All odd prime numbers are Arithmetic numbers.

1, 3, 5, 6, 7, 11, 13, 
14, 15, 17, 19, 20, 21, 22, 
23, 27, 29, 30, 31, 33, 35, 
37, 38, 39, 41, 42, 43, 44, 
45, 46, 47, 49, 51, 53, 54, 
55, 56, 57, 59, 60, 61, 62, 
65, 66, 67, 68, 69, 70, 71, 
73, 77, 78, 79, 83, 85, 86, 
87, 89, 91, 92, 93, 94, 95, 
96, 97, 99, 101, 102, 103, 105, 
107, 109, 110, 111, 113, 114, 115, 
116, 118, 119, 123, 125, 126, 127, 
129, 131, 132, 133, 134, 135, 137, 
138, 139, 140, 141, 142, 143, 145, 
147, 149, 150, 151, 153, 154, 155, 
157, 158, 159, 161, 163, 164, 165, 
166, 167, 168, 169, 173, 174, 177, 
179, 181, 182, 183, 184, 185, 186, 
187, 188, 189, 190, 191, 193, 195, 
197, 198, 199, 201, 203, 204, 205, 
206, 207, 209, 210, 211, 212, 213, 
214, 215, 217, 219, 220, 221, 222, 
223, 224, 227, 229, 230, 231, 233, 
235, 236, 237, 238, 239, 241, 245, 
246, 247, 248, 249, 251, 253, 254, 
255, 257, 258, 259, 260, 261, 262, 
263, 264, 265, 266, 267, 269, 270, 
271, 273, 275, 276, 277, 278, 280, 
281, 282, 283, 284, 285, 286, 287, 
291, 293, 294, 295, 297, 299, 301, 
302, 303, 304, 305, 307, 308, 309, 
310, 311, 313, 315, 317, 318, 319, 
321, 322, 323, 326, 327, 329, 330, 
331, 332, 334, 335, 337, 339, 340, 
341, 342, 343, 345, 347, 348, 349, 
350, 351, 352, 353, 354, 355, 356, 
357, 358, 359, 361, 365, 366, 367, 
369, 371, 373, 374, 375, 376, 377, 
378, 379, 380, 381, 382, 383, 385, 
389, 390, 393, 395, 397, 398, 
399, 401, 402, 403, 404, 406, 407, 
409, 411, 413, 414, 415, 417, 418, 
419, 420, 421, 422, 423, 425, 426, 
427, 428, 429, 430, 431, 432, 433, 
434, 435, 437, 438, 439, 443, 445, 
446, 447, 449, 451, 452, 453, 454, 
455, 456, 457, 459, 460, 461, 462, 
463, 464, 465, 467, 469, 470, 471, 
473, 474, 476, 477, 478, 479, 480, 
481, 483, 485, 486, 487, 489, 491, 
492, 493, 494, 495, 497, 498, 499, 
500, 501, 502, 503, 504, 505, 506, 
507, 509, 510, 511, 513, 515, 517, 
518, 519, 521, 523, 524, 526, 527, 
531, 533, 534, 535, 537, 539, 540, 
541, 542, 543, 545, 546, 547, 548, 
550, 551, 552, 553, 555, 557, 558, 
559, 561, 563, 564, 565, 566, 568, 
569, 570, 571, 572, 573, 574, 575, 
577, 579, 580, 581, 582, 583, 585, 
587, 589, 590, 591, 593, 594, 595, 
596, 597, 598, 599, 601, 602, 605, 
606, 607, 608, 609, 611, 612, 613, 
614, 615, 616, 617, 618, 619, 620, 
621, 622, 623, 627, 629, 630, 631, 
632, 633, 635, 636, 637, 638, 639, 
641, 642, 643, 644, 645, 646, 653, 
654, 655, 658, 659, 
660, 661, 662, 663, 665, 667, 668, 
669, 670, 671, 672, 673, 677, 678, 
679, 681, 682, 683, 685, 686, 687, 
689, 690, 691, 692, 693, 694, 695, 
697, 699, 701, 702, 703, 705, 707, 
708, 709, 710, 713, 714, 715, 716, 
717, 718, 719, 721, 723, 725, 726, 
727, 728, 731, 733, 734, 735, 736, 
737, 739, 740, 741, 742, 743, 744, 
745, 747, 748, 749, 750, 751, 753, 
755, 757, 758, 759, 761, 762, 763, 
764, 765, 766, 767, 769, 770, 771, 
773, 774, 777, 779, 780, 781, 782, 
783, 785, 786, 787, 788, 789, 790, 
791, 793, 795, 797, 798, 799, 801, 
803, 805, 806, 807, 809, 811, 812, 
813, 814, 815, 817, 820, 821, 822, 
823, 824, 825, 826, 827, 829, 830, 
831, 832, 833, 834, 835, 836, 837, 
838, 839, 840, 843, 845, 846, 849, 
851, 852, 853, 854, 855, 857, 858, 
859, 860, 861, 862, 863, 864, 865, 
869, 870, 871, 874, 875, 877, 878, 
879, 881, 883, 884, 885, 886, 887, 
889, 893, 894, 895, 897, 899, 901, 
902, 903, 905, 906, 907, 908, 909, 
910, 911, 912, 913, 915, 917, 918, 
919, 920, 921, 923, 924, 926, 929, 
930, 931, 932, 933, 934, 935, 937, 
938, 939, 940, 941, 942, 943, 944, 
945, 946, 947, 949, 950, 951, 952, 
953, 955, 956, 957, 958, 959, 961, 
963, 965, 966, 967, 969, 971, 973, 
974, 977, 978, 979, 980, 982, 983, 
985, 987, 989, 990, 991, 992, 993, 
994, 995, 996, 997, 998, 999, 

There are 727 Arithmetic numbers that are less than 1000. 223 of these Arithmetic numbers had nBABs when this collection was created.

MathBabbler wrote a C++ program to print all Arithmetic numbers between 1 and 1000.

Numbers ≥ 1000 Added Since Collection Started
1091, ..., 1011, ..., 1123, ..., 1194, ..., 1369, ..., 1393, ..., 1399, ..., 1407, ..., 1414, ..., 1429, ..., 1459, ..., 1489, ..., 1535, ..., 1597, ..., 1745, ..., 1751, ..., 1759, ..., 1789, ..., 1801, ..., 1834, ..., 1836, ..., 1838, ..., 1849, ..., 1881, ..., 1884, ..., 1888, ..., 1892, ..., 1894, ..., 1901, ..., 1907, ..., 1925, ..., 1932, ..., 1946, ..., 1949, ..., 1955, ..., 1997, ..., 2015, ..., 2017, ..., 2019, ..., 2027, ..., 2031, ..., 2033, ..., 2043, ..., 2125, ..., 2355, ..., 2551, ..., 2654, ..., 2923, ..., 2957, ..., 3023, ..., 3139, ..., 3192, ..., 3237, ..., 3435, ..., 3453, ..., 3652, ..., 3699, ..., 3828, ..., 3983, ..., 4001, ..., 4025, ..., 4033, ..., 4139, ..., 4141, ..., 4145, ..., 4199, ..., 4209, ..., 4217, ..., 4222, ..., 4242, ..., 4271, ..., 4284, ..., 4352, ..., 4399, ..., 4401, ..., 4402, ..., 4420, ..., 4444, ..., 4567, ..., 4581, ..., 4600, ..., 4699, ..., 4701, ..., 4774, ..., 4780, ..., 4799, ..., 4801, ..., 4828, ..., 4837, ..., 4875, ..., 4884, ..., 4899, ..., 4901, ..., 4949, ..., 4964, ..., 4981, ..., 5012, ..., 5015, ..., 5100, ..., 5222, ..., 5225, ..., 5252, ..., 5299, ..., 5310, ..., 5449, ..., 5478, ..., 5479, ..., 5522, ..., 5600, ..., 5695, ..., 5719, ..., 5950, ..., 5962, ..., 6068, ..., 6999, ..., 7007, ..., 7100, ..., 7355, ..., 7534, ..., 7776, ..., 7798, ..., 7842, ..., 8500, ..., 8558, ..., 9241, ..., 9871, ..., 9999, ..., 15151, ..., 15451, ..., 15551, ..., 19191, ..., 19519, ..., 19591, ..., 19691, ..., 19791, ..., 19891, ..., 19991, ..., 20097, ..., 21000, ..., 21116, ..., 21129, ..., 21419, ..., 21420, ..., 21734, ..., 25915, ..., 27028, ..., 27572, ..., 27772, ..., 28382, ..., 31777, ..., 32142, ..., 32228, ..., 32230, ..., 32543, ..., 33433, ..., 36254, ..., 37621, ..., 51015, ..., 51115, ..., 51215, ..., 51315, ..., 51415, ..., 51515, ..., 51615, ..., 51654, ..., 51715, ..., 51815, ..., 51915, ..., 55055, ..., 55155, ..., 55255, ..., 55355, ..., 55455, ..., 55555, ..., 55655, ..., 55755, ..., 55855, ..., 55955, ..., 61016, ..., 61116, ..., 61316, ..., 61420, ..., 61816, ..., 61916, ..., 62374, ..., 62379, ..., 63736, ..., 63836, ..., 64064, ..., 64264, ..., 64446, ..., 64546, ..., 64646, ..., 64746, ..., 64846, ..., 64946, ..., 65056, ..., 65156, ..., 65256, ..., 65756, ..., 65956, ..., 66066, ..., 66166, ..., 66366, ..., 66466, ..., 66566, ..., 66666, ..., 67176, ..., 67576, ..., 67676, ..., 67777, ..., 67876, ..., 68386, ..., 68486, ..., 68586, ..., 68686, ..., 68786, ..., 68886, ..., 69096, ..., 69396, ..., 69465, ..., 69496, ..., 69596, ..., 70007, ..., 70107, ..., 70207, ..., 70307, ..., 70407, ..., 70507, ..., 70607, ..., 70707, ..., 70807, ..., 70907, ..., 71017, ..., 71117, ..., 71217, ..., 71317, ..., 71417, ..., 71517, ..., 71617, ..., 71717, ..., 71817, ..., 71917, ..., 72027, ..., 72127, ..., 72227, ..., 72327, ..., 72427, ..., 72527, ..., 72627, ..., 72727, ..., 72827, ..., 72927, ..., 73037, ..., 73137, ..., 73237, ..., 73337, ..., 73537, ..., 73637, ..., 73737, ..., 73837, ..., 73937, ..., 74047, ..., 74147, ..., 74247, ..., 74347, ..., 74447, ..., 74547, ..., 74647, ..., 74747, ..., 74847, ..., 74947, ..., 75057, ..., 75065, ..., 75157, ..., 75257, ..., 75357, ..., 75457, ..., 75557, ..., 75657, ..., 75757, ..., 75857, ..., 75957, ..., 76067, ..., 76167, ..., 76267, ..., 76367, ..., 76467, ..., 76567, ..., 76667, ..., 76767, ..., 76867, ..., 76967, ..., 77177, ..., 77277, ..., 77377, ..., 77477, ..., 77577, ..., 77677, ..., 77877, ..., 77977, ..., 78087, ..., 78187, ..., 78287, ..., 78387, ..., 78487, ..., 78587, ..., 78787, ..., 78887, ..., 78987, ..., 79097, ..., 79197, ..., 79297, ..., 79397, ..., 79597, ..., 79697, ..., 79797, ..., 79897, ..., 79997, ..., 80108, ..., 80308, ..., 80608, ..., 80708, ..., 80808, ..., 80908, ..., 81018, ..., 81118, ..., 81318, ..., 81518, ..., 81618, ..., 81718, ..., 81818, ..., 81918, ..., 82028, ..., 82128, ..., 82428, ..., 82528, ..., 82628, ..., 82728, ..., 83038, ..., 83138, ..., 83238, ..., 83438, ..., 83538, ..., 83638, ..., 83738, ..., 83838, ..., 84348, ..., 84448, ..., 84548, ..., 84648, ..., 84948, ..., 85058, ..., 85158, ..., 85258, ..., 85337, ..., 85358, ..., 85458, ..., 85558, ..., 85620, ..., 85758, ..., 85958, ..., 86368, ..., 86668, ..., 86968, ..., 87078, ..., 87178, ..., 87278, ..., 87378, ..., 87478, ..., 87678, ..., 87878, ..., 87978, ..., 88088, ..., 88188, ..., 88288, ..., 88388, ..., 88988, ..., 89998, ..., 89198, ..., 89398, ..., 89598, ..., 89698, ..., 89798, ..., 89898, ..., 90009, ..., 90109, ..., 90209, ..., 90309, ..., 90409, ..., 90509, ..., 90609, ..., 90709, ..., 90809, ..., 90909, ..., 91019, ..., 91119, ..., 91219, ..., 91319, ..., 91419, ..., 91420, ..., 91519, ..., 91619, ..., 91719, ..., 91819, ..., 91919, ..., 91997, ..., 92003, ..., 92009, ..., 92129, ..., 92229, ..., 92329, ..., 92429, ..., 92529, ..., 92629, ..., 92729, ..., 92829, ..., 92929, ..., 93039, ..., 93139, ..., 93239, ..., 93339, ..., 93439, ..., 93539, ..., 93739, ..., 93839, ..., 93939, ..., 94049, ..., 94149, ..., 94249, ..., 94349, ..., 94449, ..., 94549, ..., 94649, ..., 94749, ..., 94849, ..., 94949, ..., 95059, ..., 95159, ..., 95259, ..., 95359, ..., 95459, ..., 95559, ..., 95759, ..., 95959, ..., 96069, ..., 96169, ..., 96269, ..., 96369, ..., 96469, ..., 96569, ..., 96669, ..., 96769, ..., 96869, ..., 96969, ..., 97079, ..., 97147, ..., 97179, ..., 97279, ..., 97379, ..., 97579, ..., 97679, ..., 97779, ..., 97879, ..., 97979, ..., 98089, ..., 98189, ..., 98389, ..., 98489, ..., 98589, ..., 98689, ..., 98789, ..., 98889, ..., 98989, ..., 99199, ..., 99299, ..., 99399, ..., 99499, ..., 99599, ..., 99699, ..., 99799, ..., 99899, ..., 99999, ..., 100001, ..., 101010, ..., 101101, ..., 101101, ..., 102201, ..., 103301, ..., 104401, ..., 105501, ..., 106601, ..., 107701, ..., 108801, ..., 109901, ..., 110011, ..., 111111, ..., 112211, ..., 113311, ..., 137017, ... 221559, ... 241242, ... 420420, ...

Creator: Gerald Thurman [gthurman@gmail.com]
Created: 31 December 2014
Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 United States License.


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