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aban n.  and  Duffinian n.

First numbers that belong to both sets:

4, 8, 9, 16, 21, 25, 27, 32, 35, 36, 39, 49, 50, 55, 57, 63, 64, 65, 75, 77, 81, 85, 93, 98, 100, 111, 115, 119, 121, 125, 128, 129, 133, 143, 144, 155, 161, 169, 171, 175, 183, 185, 187, 189, 201, 203, 205, 209, 215, 217, 219, 221, 225, 235, 237, 242, 243, 245, 247, 253, 256, 259, 265, 275, 279, 289, 291, 299, 301, 305, 309, 319, 323, 324, 325, 327, 329, 333, 335, 338, 341, 343, 351, 355, 361, 363, 365, 371, 377, 381, 385, 387, 391, 392, 399, 400, 403, 407, 413, 415, 417, 425, 427, 437, 451, 453, 469, 471, 481, 484, 485, 489, 493, 497, 505, 511, 512, 513, 515, 517, 525, 527, 529, 533, 535, 539, 543, 549, 551, 553, 559, 565, 567, 575, 576, 578, 579, 583, 589, 595, 597, 603, 605, 611, 623, 625, 629, 633, 635, 649, 651, 655, 657, 667, 669, 671, 676, 685, 687, 689, 697, 707, 711, 713, 715, 721, 722, 723, 729, 731, 737, 741, 749, 755, 763, 767, 777, 779, 781, 784, 785, 791, 793, 799, 800, 803, 805, 813, 815, 817, 831, 833, 835, 837, 841, 845, 849, 851, 865, 867, 869, 871, 873, 875, 889, 893, 899, 900, 901, 903, 905, 913, 917, 921, 923, 925, 927, 935, 939, 943, 949, 955, 959, 961, 965, 968, 975, 979, 981, 985, 989, 993, 999, 1000000, 1000001, 1000007, 1000009, 1000011, 1000013, 1000015, 1000019, 1000021, 1000027, 1000029, 1000031, 1000043, 1000047, 1000049, 1000051, 1000053, 1000057, 1000061, 1000063, 1000067, 1000069, 1000073, 1000079, 1000083, 1000085, 1000087, 1000089, 1000091, 1000093, 1000097, 1000101, 1000103, 1000109, 1000111, 1000115, 1000123, 1000127, 1000129, 1000135, 1000137, 1000141, 1000143, 1000147, 1000157, 1000163, 1000165.

Some larger examples :