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sphenic n.  and  star n.

First numbers that belong to both sets:

8437, 9361, 15301, 31537, 35113, 51337, 66781, 70633, 80041, 103753, 125281, 134101, 143221, 150733, 168337, 176473, 195481, 199837, 220033, 224653, 231673, 263341, 278641, 289081, 297037, 299713, 302401, 324337, 370513, 394753, 397837, 404041, 410293, 439021, 452101, 478837, 506341, 513337, 516853, 541801, 545413, 552673, 559981, 601033, 627913, 679393, 687493, 741313, 754021, 762553, 784093, 828073, 846001, 855037, 859573, 868681, 910261, 948037, 967213, 972037, 1006141, 1030861, 1060921, 1081201, 1111981, 1132741, 1169533, 1180153, 1185481, 1196173, 1233973, 1362313, 1373773, 1385281, 1402633, 1473121, 1551433, 1575937, 1613053, 1631773, 1638037, 1644313, 1694953, 1714141, 1720561, 1733437, 1778881, 1785421, 1831537, 1858153, 1864837, 1884961, 1932337, 1939153, 2007973, 2056861, 2070937, 2099233, 2134873, 2149213, 2243593, 2347501, 2362537, 2392753, 2407933, 2446093, 2538901, 2546713, 2562373, 2578081, 2609641, 2617561, 2665333, 2697421, 2721613, 2754037, 2803033, 2827693, 2885653, 2919037, 2927413, 2944201, 3028861, 3080233, 3097453, 3106081, 3263437, 3281161, 3316753, 3580537, 3664453, 3730393, 3825613, 3835201, 3902653, 3951193, 4009837, 4168333, 4319713, 4370773, 4391281, 4411837, 4473793, 4515337, 4567537, 4578013, 4599001, 4651681, 4704661, 4725937, 4757941, 4811521, 4843813, 4897873, 4952233, 5017861, 5106037, 5128201, 5150413, 5194981, 5262193, 5273437, 5295961, 5409301, 5420701, 5443537, 5523841, 5535361, 5546893, 5581561, 5593141, 5791837, 5815441, 5934181, 5958073, 5994001, 6066181, 6102433, 6150937, 6163093, 6199633, 6236281, 6346873, 6359221, 6396337, 6495841, 6508333, 6596113, 6671821, 6798961, 6888673, 6927301, 7017853, 7043833, 7135141, 7148233, 7319521, 7425937, 7519681, 7533121, 7614013, 7641073, 7654621, 7695337, 7763437, 7831837, 7845553, 7859281, 8011081, 8052733, 8094493, 8136361, 8220421, 8234473, 8248537, 8446693, 8489461, 8532337, 8589673, 8647201, 9011101, 9040537, 9129133, 9173593, 9188437, 9277753, 9322573, 9337537, 9502933, 9548293, 9669781, 9715537, 9761401, 9868837, 9992341, 10023337, 10038853, 10179037, 10210321, 10288741, 10320193, 10351693, 10414837, 10525801, 10573537, 10653337, 10685341, 10829953, 10878373, 10943101, 11056837, 11154793, 11203933, 11236753, 11302537, 11368513, 11418121, 11451253, 11517661, 11534293, 11584261, 11600941, 11617633, 11634337, 11701273, 11785213, 11920141, 12004861, 12089881, 12158113, 12192301, 12243673, 12295153, 12450241, 12467533, 12484837, 12519481, 12536821, 12675973, 12710881.

Some larger examples :