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amenable n.  and  weak prime

First numbers that belong to both sets:

13, 61, 73, 89, 109, 113, 181, 193, 229, 233, 241, 293, 313, 317, 337, 349, 353, 389, 401, 409, 421, 433, 449, 509, 577, 601, 661, 677, 709, 761, 773, 797, 829, 941, 953, 997, 1013, 1021, 1033, 1069, 1093, 1097, 1109, 1129, 1153, 1193, 1201, 1217, 1237, 1321, 1373, 1381, 1409, 1429, 1433, 1453, 1489, 1493, 1553, 1601, 1609, 1613, 1621, 1637, 1669, 1709, 1789, 1873, 1889, 1913, 1933, 2017, 2029, 2069, 2089, 2113, 2161, 2213, 2221, 2269, 2273, 2297, 2341, 2357, 2393, 2441, 2477, 2557, 2593, 2621, 2633, 2689, 2693, 2713, 2753, 2777, 2837, 2861, 2909, 2917, 2957, 3001, 3041, 3049, 3089, 3121, 3137, 3169, 3209, 3221, 3229, 3253, 3301, 3361, 3373, 3413, 3469, 3517, 3529, 3533, 3541, 3593, 3617, 3673, 3677, 3701, 3709, 3769, 3797, 3833, 3853, 3881, 3889, 4021, 4057, 4093, 4129, 4133, 4177, 4261, 4273, 4289, 4297, 4373, 4397, 4493, 4549, 4733, 4789, 4793, 4801, 4817, 4877, 4889, 4909, 4933, 4937, 4957, 4969, 4973, 5081, 5101, 5153, 5197, 5209, 5233, 5237, 5281, 5309, 5333, 5449, 5521, 5573, 5581, 5641, 5653, 5669, 5693, 5701, 5717, 5749, 5813, 5861, 5869, 5881, 5953, 6053, 6101, 6121, 6133, 6173, 6221, 6229, 6277, 6301, 6329, 6361, 6397, 6473, 6481, 6529, 6553, 6581, 6661, 6709, 6737, 6781, 6793, 6829, 6833, 6841, 6917, 6949, 6961, 7001, 7109, 7129, 7193, 7213, 7253, 7309, 7333, 7369, 7417, 7433, 7481, 7489, 7529, 7541, 7549, 7561, 7577, 7621, 7649, 7673, 7793, 7829, 7853, 7937, 8017, 8069, 8089, 8093, 8101, 8221, 8233, 8237, 8273, 8293, 8297, 8317, 8329, 8369, 8377, 8389, 8581, 8609, 8629, 8669, 8681, 8693, 8741, 8753, 8761, 8821, 8849, 8893, 8933, 8941, 9001, 9013, 9049, 9109, 9137, 9161, 9209, 9241, 9257, 9293, 9349.

Some larger examples :