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Hogben n.  and  sphenic n.

First numbers that belong to both sets:

273, 651, 1407, 2163, 2451, 3081, 3423, 3783, 4161, 5551, 6643, 7657, 7833, 8931, 10507, 11343, 11557, 11991, 14043, 17031, 17823, 18361, 18907, 19461, 20307, 20881, 22351, 22953, 23871, 25123, 25441, 25761, 28731, 32943, 34041, 37443, 38613, 39403, 42231, 43473, 47307, 48621, 49063, 52671, 53131, 54057, 56883, 58807, 61257, 62751, 64263, 64771, 68907, 72093, 72631, 74803, 79807, 80373, 80941, 84973, 87321, 87913, 89103, 90903, 92721, 93331, 94557, 96411, 102081, 104007, 106603, 107913, 109893, 113907, 115941, 117993, 120063, 120757, 122151, 125671, 126381, 129241, 132861, 134323, 135057, 135793, 138757, 144021, 146307, 150157, 153273, 154843, 155631, 157213, 158007, 160401, 162813, 166873, 170157, 172641, 174307, 175143, 180201, 181051, 185331, 186193, 187923, 192283, 201153, 202951, 203853, 206571, 209307, 210223, 214833, 215761, 221371, 228963, 231843, 235711, 237657, 244531, 247507, 252507, 255531, 256543, 263683, 273007, 274053, 278257, 283557, 286761, 287833, 293223, 295393, 296481, 299757, 303051, 305257, 308581, 323193, 331201, 332353, 333507, 348691, 353431, 354621, 355813, 358203, 361803, 365421, 369057, 370273, 372711, 376383, 377611, 378841, 383781, 385021, 393757, 398793, 400057, 407683, 408961, 414093, 420553, 425757, 432307, 441561, 449571, 452257, 454951, 461721, 464443, 469911, 472657, 474033, 478173, 479557, 482331, 483721, 486507, 494913, 499143, 500557, 503391, 506233, 510511, 520563, 532171, 533631, 538023, 545383, 546861, 551307, 554281, 555771, 560253, 563251, 564753, 573807, 578361, 582933, 592131, 599851, 607621, 609181, 615441, 618583, 629643, 634413, 640801, 648831, 653673, 668307, 673221, 674863, 679801, 683103, 688071, 701407, 706441, 709807, 713181, 718257, 728463, 737023, 742183, 749091, 750823, 757771, 759513, 763003, 764751, 782341, 785883, 796557, 812703, 823557, 825373, 834483, 836311, 854701, 858403, 867693, 873291, 880783, 882661, 888307, 897757, 911071, 912981, 916807, 918723, 936057, 941871, 943813, 947703, 951601, 953553, 959421, 969241, 971211, 977133, 979111, 991021, 993013, 1011031, 1019091, 1025157, 1031241, 1037343, 1047553, 1051651, 1053703, 1063993, 1076407, 1078483, 1082641, 1086807.

Some larger examples :