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amenable n.  and  gapful n.

First numbers that belong to both sets:

100, 105, 108, 120, 121, 132, 140, 160, 165, 176, 180, 192, 200, 220, 225, 240, 253, 260, 264, 280, 297, 300, 341, 352, 360, 385, 396, 400, 405, 440, 473, 480, 484, 500, 561, 572, 600, 660, 693, 700, 781, 792, 800, 880, 900, 1000, 1001, 1005, 1008, 1020, 1032, 1037, 1040, 1053, 1056, 1060, 1064, 1065, 1080, 1092, 1100, 1120, 1125, 1136, 1140, 1152, 1160, 1180, 1185, 1188, 1200, 1204, 1212, 1216, 1220, 1221, 1240, 1245, 1260, 1272, 1280, 1296, 1300, 1305, 1313, 1320, 1332, 1340, 1344, 1349, 1360, 1365, 1368, 1376, 1377, 1380, 1392, 1400, 1420, 1425, 1440, 1441, 1452, 1456, 1460, 1480, 1484, 1485, 1500, 1512, 1520, 1536, 1540, 1545, 1548, 1560, 1572, 1573, 1580, 1600, 1605, 1616, 1620, 1624, 1632, 1640, 1660, 1661, 1665, 1680, 1692, 1696, 1700, 1717, 1720, 1725, 1728, 1729, 1740, 1752, 1760, 1764, 1776, 1780, 1785, 1800, 1812, 1820, 1833, 1840, 1845, 1856, 1860, 1872, 1880, 1881, 1900, 1904, 1905, 1908, 1920, 1932, 1936, 1940, 1960, 1965, 1980, 1992, 2000, 2020, 2025, 2040, 2060, 2064, 2080, 2093, 2100, 2112, 2120, 2121, 2125, 2128, 2140, 2160, 2180, 2184, 2200, 2220, 2225, 2236, 2240, 2260, 2268, 2280, 2300, 2304, 2320, 2325, 2332, 2340, 2349, 2360, 2380, 2400, 2408, 2420, 2424, 2425, 2440, 2457, 2460, 2480, 2496, 2500, 2520, 2525, 2540, 2541, 2544, 2548, 2552, 2553, 2560, 2580, 2600, 2620, 2625, 2640, 2660, 2664, 2680, 2688, 2700, 2720, 2725, 2740, 2756, 2760, 2772, 2780, 2784, 2800, 2820, 2825, 2828, 2840, 2860, 2880, 2900, 2904, 2920, 2925, 2929, 2940, 2960, 2961, 2968, 2980, 2992, 2997, 3000, 3045, 3060, 3072, 3096, 3120, 3180, 3185, 3232, 3240, 3264, 3268, 3276, 3300, 3325, 3333, 3360, 3392, 3420, 3441.

Some larger examples :