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amenable n.  and  Poulet n.

First numbers that belong to both sets:

341, 561, 645, 1105, 1729, 1905, 2465, 2701, 2821, 3277, 4033, 4369, 4681, 5461, 6601, 7957, 8321, 8481, 10261, 10585, 11305, 12801, 13741, 13981, 15709, 15841, 16705, 18705, 18721, 23001, 23377, 25761, 29341, 30121, 30889, 31417, 31609, 31621, 33153, 34945, 35333, 39865, 41041, 41665, 46657, 49141, 49981, 52633, 55245, 57421, 60701, 62745, 63973, 65077, 65281, 68101, 72885, 74665, 75361, 80581, 83333, 83665, 85489, 87249, 88357, 88561, 91001, 93961, 101101, 104653, 107185, 113201, 115921, 121465, 126217, 129889, 129921, 130561, 137149, 149281, 154101, 157641, 158369, 162193, 162401, 164737, 172081, 176149, 181901, 188057, 188461, 194221, 196021, 196093, 204001, 206601, 208465, 212421, 215265, 215749, 219781, 220729, 223345, 226801, 228241, 233017, 241001, 249841, 252601, 253241, 264773, 266305, 276013, 278545, 280601, 282133, 284581, 285541, 289941, 294409, 314821, 318361, 323713, 332949, 334153, 340561, 341497, 348161, 357761, 367081, 390937, 399001, 401401, 410041, 423793, 427233, 448921, 449065, 451905, 458989, 464185, 481573, 486737, 488881, 489997, 493697, 493885, 512461, 513629, 526593, 530881, 534061, 552721, 556169, 563473, 574561, 574861, 580337, 582289, 587861, 588745, 604117, 611701, 617093, 622909, 625921, 635401, 642001, 647089, 653333, 656601, 657901, 658801, 665281, 665333, 665401, 670033, 679729, 683761, 688213, 710533, 711361, 721801, 722201, 722261, 729061, 738541, 742813, 743665, 745889, 748657, 757945, 769757, 786961, 800605, 818201, 825265, 831405, 838201, 838861, 841681, 847261, 852481, 852841, 873181, 875161, 898705, 915981, 934021, 950797, 976873, 983401, 997633, 1004653, 1016801, 1018921, 1023121, 1033669, 1050985, 1052929, 1053761, 1064053, 1073021, 1082401, 1082809, 1093417, 1104349, 1106785, 1109461, 1128121, 1132657, 1139281, 1141141, 1145257, 1157689, 1168513, 1193221, 1194649, 1207361, 1246785, 1251949, 1252697, 1275681, 1293337, 1306801, 1333333, 1357441, 1357621, 1373653, 1394185, 1398101, 1457773, 1461241, 1463749, 1472065, 1472353, 1472505, 1485177, 1489665, 1493857, 1500661, 1507561, 1509709, 1520905, 1529185, 1533601, 1533961, 1534541, 1537381, 1569457, 1579249, 1584133, 1608465, 1615681, 1620385, 1643665, 1678541, 1690501, 1711381, 1719601.

Some larger examples :