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binomial coefficient  and  sphenic n.

First numbers that belong to both sets:

66, 70, 78, 105, 165, 190, 231, 286, 406, 435, 455, 465, 561, 595, 715, 741, 861, 903, 946, 969, 1001, 1378, 1653, 1771, 2211, 2278, 2485, 3081, 3655, 3741, 4371, 4465, 4495, 5151, 5253, 5995, 6441, 7021, 7503, 8515, 8911, 9139, 9453, 9591, 10011, 10153, 10585, 11026, 12341, 12561, 13366, 14878, 15051, 15753, 16471, 18145, 20301, 20503, 21115, 22366, 22791, 23005, 23653, 23871, 24753, 26335, 28441, 32131, 32509, 33153, 36046, 39621, 39903, 40186, 42778, 44551, 45451, 45753, 48205, 50086, 50403, 53301, 54946, 55945, 62481, 67161, 69751, 72771, 75466, 77421, 77815, 80601, 83845, 87571, 92665, 93961, 96141, 97903, 99235, 99681, 102831, 115921, 124251, 125751, 129286, 132355, 137026, 138601, 144453, 147153, 149878, 153181, 154846, 159895, 176851, 179101, 180901, 183921, 190653, 191271, 193753, 200661, 201295, 205761, 206403, 208981, 212878, 213531, 216811, 229503, 232903, 239086, 241165, 243253, 243951, 249571, 251695, 257403, 275653, 277885, 289941, 293761, 298378, 303031, 309291, 310078, 314821, 317206, 322003, 334153, 337431, 338253, 341551, 344035, 354903, 364231, 374545, 385881, 403651, 410871, 411778, 417241, 424581, 425503, 435711, 437989, 439453, 443211, 447931, 459361, 470935, 473851, 477753, 506521, 509545, 521731, 530965, 534061, 539241, 542361, 543403, 547581, 552826, 571915, 584821, 590241, 594595, 607753, 614386, 621055, 624403, 631126, 637885, 646953, 648091, 651511, 657359, 675703, 686206, 697971, 712221, 718201, 723003, 747253, 752151, 754606, 791911, 795691, 796953, 826255, 836571, 841753, 867903, 905185, 906531, 917335, 926841, 939929, 943251, 955653, 977901, 982101, 983503, 1004653, 1017451, 1027461, 1033203, 1046181, 1073845, 1091503, 1109305, 1113778, 1122751, 1127251, 1140805, 1145341, 1172746, 1181953, 1189653, 1214461, 1233235, 1245831, 1252153, 1276003, 1290421, 1301691, 1316253, 1322751, 1339066, 1347261, 1348903, 1368685, 1381953, 1393615, 1408681, 1440753, 1442451, 1456071, 1468041, 1474903, 1485226, 1490401, 1500778, 1516411, 1546161, 1551441, 1553203, 1558495, 1579753, 1595791, 1601155, 1622701, 1638955, 1658931, 1688203, 1690041, 1704781, 1725153, 1741911, 1743778.

Some larger examples :