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Poulet n.  and  sphenic n.

First numbers that belong to both sets:

561, 645, 1105, 1729, 1905, 2465, 2821, 4371, 6601, 8481, 8911, 10585, 12801, 13741, 13981, 15841, 16705, 25761, 29341, 30121, 30889, 33153, 34945, 41665, 46657, 52633, 57421, 68101, 74665, 83665, 87249, 88561, 91001, 93961, 113201, 115921, 121465, 137149, 149281, 154101, 158369, 162401, 176149, 196021, 204001, 206601, 208465, 223345, 228241, 252601, 258511, 276013, 284581, 285541, 289941, 294409, 314821, 323713, 334153, 341497, 348161, 387731, 399001, 410041, 423793, 427233, 448921, 476971, 488881, 493697, 512461, 526593, 530881, 534061, 563473, 574561, 574861, 588745, 617093, 625921, 635401, 665401, 683761, 711361, 738541, 841681, 847261, 852481, 950797, 1004653, 1018921, 1023121, 1024651, 1052503, 1052929, 1093417, 1104349, 1128121, 1141141, 1152271, 1193221, 1306801, 1333333, 1357621, 1398101, 1419607, 1459927, 1461241, 1463749, 1472353, 1500661, 1507561, 1529185, 1533601, 1534541, 1549411, 1615681, 1643665, 1746289, 1801969, 1827001, 1839817, 1840357, 1857241, 1896961, 1907851, 1909001, 2085301, 2121301, 2144521, 2162721, 2165801, 2171401, 2233441, 2290641, 2299081, 2327041, 2350141, 2419385, 2508013, 2537641, 2603381, 2609581, 2626177, 2773981, 2780731, 2899801, 2940337, 2953711, 2987167, 3048841, 3057601, 3073357, 3186821, 3225601, 3316951, 3336319, 3581761, 3679201, 3763801, 3814357, 3828001, 3936691, 4014361, 4038673, 4069297, 4072729, 4154977, 4209661, 4259905, 4335241, 4504501, 4650049, 4682833, 4714201, 4827613, 4864501, 4877641, 4917331, 4974971, 5049001, 5148001, 5271841, 5400489, 5444489, 5456881, 5481451, 5551201, 5599765, 5681809, 5733649, 5758273, 5859031, 5968873, 6183601, 6189121, 6236473, 6255341, 6350941, 6474691, 6617929, 6733693, 6868261, 6998881, 7207201, 7273267, 7416289, 7455709, 7516153, 7519441, 7656721, 7803769, 7814401, 8043841, 8134561, 8137585, 8137633, 8209657, 8321671, 8640661, 8812273, 8916251, 9046297, 9069229, 9084223, 9143821, 9345541, 9439201, 9692453, 10024561, 10079521, 10185841, 10251473, 10267951, 10513261, 10545991, 10635751, 10700761, 10802017, 10958221, 11157721, 11328409, 11644921, 11972017, 12096613, 12407011, 12599233, 12783811, 12932989, 12936763, 13421773, 13554781, 13635649, 13942081, 14012797, 14154337, 14469841, 14609401, 14671801, 14676481, 14684209, 14898631, 14913991, 15082901, 15124969, 15162941, 15247621, 15510041, 15603391, 15700301, 15732721, 15829633, 16053193, 16149169, 16153633, 16539601, 16666651, 16998961, 17020201, 17098369.

Some larger examples :