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amenable n.  and  Hogben n.

First numbers that belong to both sets:

1, 13, 21, 57, 73, 133, 157, 241, 273, 381, 421, 553, 601, 757, 813, 993, 1057, 1261, 1333, 1561, 1641, 1893, 1981, 2257, 2353, 2653, 2757, 3081, 3193, 3541, 3661, 4033, 4161, 4557, 4693, 5113, 5257, 5701, 5853, 6321, 6481, 6973, 7141, 7657, 7833, 8373, 8557, 9121, 9313, 9901, 10101, 10713, 10921, 11557, 11773, 12433, 12657, 13341, 13573, 14281, 14521, 15253, 15501, 16257, 16513, 17293, 17557, 18361, 18633, 19461, 19741, 20593, 20881, 21757, 22053, 22953, 23257, 24181, 24493, 25441, 25761, 26733, 27061, 28057, 28393, 29413, 29757, 30801, 31153, 32221, 32581, 33673, 34041, 35157, 35533, 36673, 37057, 38221, 38613, 39801, 40201, 41413, 41821, 43057, 43473, 44733, 45157, 46441, 46873, 48181, 48621, 49953, 50401, 51757, 52213, 53593, 54057, 55461, 55933, 57361, 57841, 59293, 59781, 61257, 61753, 63253, 63757, 65281, 65793, 67341, 67861, 69433, 69961, 71557, 72093, 73713, 74257, 75901, 76453, 78121, 78681, 80373, 80941, 82657, 83233, 84973, 85557, 87321, 87913, 89701, 90301, 92113, 92721, 94557, 95173, 97033, 97657, 99541, 100173, 102081, 102721, 104653, 105301, 107257, 107913, 109893, 110557, 112561, 113233, 115261, 115941, 117993, 118681, 120757, 121453, 123553, 124257, 126381, 127093, 129241, 129961, 132133, 132861, 135057, 135793, 138013, 138757, 141001, 141753, 144021, 144781, 147073, 147841, 150157, 150933, 153273, 154057, 156421, 157213, 159601, 160401, 162813, 163621, 166057, 166873, 169333, 170157, 172641, 173473, 175981, 176821, 179353, 180201, 182757, 183613, 186193, 187057, 189661, 190533, 193161, 194041, 196693, 197581, 200257, 201153, 203853, 204757, 207481, 208393, 211141, 212061, 214833, 215761, 218557, 219493, 222313, 223257, 226101, 227053, 229921, 230881, 233773, 234741, 237657, 238633, 241573, 242557, 245521, 246513, 249501, 250501, 253513, 254521, 257557, 258573, 261633, 262657, 265741, 266773, 269881, 270921, 274053, 275101, 278257, 279313, 282493, 283557, 286761, 287833, 291061, 292141, 295393, 296481, 299757, 300853, 304153, 305257, 308581, 309693, 313041.

Some larger examples :