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odious n.  and  Poulet n.

First numbers that belong to both sets:

341, 1387, 1729, 1905, 2047, 2465, 2821, 3277, 4033, 4371, 4681, 5461, 6601, 8321, 10261, 10585, 13741, 13747, 13981, 15841, 18705, 18721, 19951, 23001, 29341, 30121, 31609, 31621, 35333, 41041, 46657, 49141, 49981, 52633, 55245, 57421, 60787, 62745, 63973, 65077, 65281, 68101, 72885, 75361, 80581, 83333, 90751, 93961, 104653, 113201, 121465, 126217, 129889, 130561, 137149, 149281, 154101, 162193, 162401, 176149, 181901, 188057, 196021, 196093, 204001, 208465, 212421, 215749, 219781, 220729, 223345, 228241, 241001, 249841, 258511, 271951, 272251, 275887, 276013, 289941, 294409, 318361, 323713, 348161, 357761, 367081, 387731, 399001, 401401, 410041, 422659, 448921, 451905, 458989, 476971, 486737, 489997, 493697, 493885, 513629, 514447, 530881, 552721, 556169, 563473, 574561, 574861, 580337, 611701, 617093, 622909, 625921, 642001, 647089, 658801, 665333, 670033, 679729, 688213, 710533, 722261, 729061, 738541, 743665, 745889, 748657, 769757, 786961, 825265, 831405, 838861, 847261, 852481, 852841, 875161, 898705, 916327, 934021, 983401, 997633, 1016801, 1023121, 1024651, 1050985, 1053761, 1073021, 1082401, 1082809, 1106785, 1128121, 1145257, 1246785, 1251949, 1252697, 1275681, 1277179, 1293337, 1302451, 1306801, 1333333, 1357441, 1373653, 1397419, 1398101, 1441091, 1457773, 1461241, 1463749, 1472505, 1493857, 1507561, 1507963, 1529185, 1530787, 1533601, 1533961, 1537381, 1549411, 1569457, 1579249, 1584133, 1615681, 1690501, 1719601, 1735841, 1746289, 1755001, 1801969, 1809697, 1815465, 1826203, 1830985, 1839817, 1896961, 1907851, 1908985, 1969417, 1993537, 1994689, 2004403, 2008597, 2081713, 2113921, 2142141, 2163001, 2165801, 2181961, 2213121, 2233441, 2264369, 2299081, 2313697, 2350141, 2414001, 2433601, 2434651, 2503501, 2508013, 2528921, 2537641, 2609581, 2615977, 2617451, 2649029, 2649361, 2704801, 2746589, 2748023, 2773981, 2780731, 2793351, 2867221, 2882265, 2899801, 2909197, 2940337, 2944261, 2953711, 2987167, 3073357, 3090091, 3094273, 3146221, 3165961, 3186821, 3224065, 3225601, 3316951, 3375487, 3429037, 3435565, 3539101, 3542533, 3567481, 3568661, 3581761, 3656449, 3726541, 3755521, 3763801, 3814357, 3898129, 3916261, 3936691, 3985921, 4005001, 4025905, 4038673, 4069297, 4072729, 4082653, 4101637, 4151869, 4154161, 4154977, 4181921, 4209661, 4314967, 4363261, 4371445.

Some larger examples :