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interprime n.  and  Zuckerman n.

First numbers that belong to both sets:

4, 6, 9, 12, 15, 111, 144, 312, 315, 432, 816, 1113, 1176, 1184, 1197, 1344, 1416, 1575, 1715, 2112, 3168, 4224, 9315, 11115, 11172, 12312, 13311, 13932, 16632, 21216, 23424, 24912, 26112, 26712, 31131, 32616, 32832, 41232, 42912, 51975, 83232, 86112, 111135, 111168, 112116, 112416, 113328, 116172, 117264, 121716, 123264, 123732, 131112, 131712, 139968, 141912, 143112, 149112, 181248, 182784, 183312, 186624, 196128, 214144, 291168, 312732, 317184, 331344, 336312, 373212, 413112, 422112, 434112, 437472, 611112, 711312, 731115, 831312, 842112, 1111212, 1112832, 1114176, 1116216, 1131264, 1131711, 1131732, 1132416, 1141248, 1141632, 1167264, 1177176, 1181712, 1212224, 1212912, 1221912, 1231272, 1271424, 1274112, 1281216, 1283328, 1319328, 1349136, 1411992, 1412224, 1413216, 1418112, 1621296, 1632312, 1634112, 1638144, 1641312, 1772232, 1818624, 1878912, 2111172, 2112192, 2121192, 2121984, 2127216, 2141136, 2184192, 2212224, 2221632, 2234112, 2241312, 2247168, 2311632, 2416128, 2431296, 2471616, 2473632, 2483712, 2619216, 2794176, 2842112, 3112128, 3128832, 3138912, 3164112, 3184128, 3186432, 3222144, 3262464, 3317328, 3441312, 3482112, 3618432, 3642624, 3921372, 4117176, 4121712, 4197312, 4221312, 4271232, 4311216, 4368384, 4921344, 5751375, 6116112, 6132672, 6161112, 6612192, 7133112, 7322112, 7334712, 8617728, 8733312, 9212112, 9222336, 9431424, 9813312, 11111292, 11111424, 11112912, 11114496, 11116224, 11119113, 11141112, 11142144, 11151175, 11166336, 11184192, 11186112, 11191311, 11211132, 11211312, 11212992, 11261232, 11293344, 11311344, 11319912, 11373264, 11411112, 11417112, 11423232, 11429712, 11441664, 11687424, 11688192, 11739168, 11741184, 11826432, 12111312, 12113472, 12121112, 12123648, 12143712, 12146112, 12161232, 12212112, 12218112, 12236112, 12313728, 12344832, 12714912, 12743136, 12911472, 13149216, 13211112, 13272336, 13311135, 13412112, 13442112, 13622112, 13647312, 14211792, 14711424, 16214112, 16221312, 16441344, 16611264, 16948224, 17192448, 17223192, 17231424, 17313912, 17412192, 18477312, 18717216, 18746112, 18914112, 19191168, 21112112, 21113136, 21131112, 21131712, 21134112, 21161232, 21192192, 21236112, 21272832, 21282816, 21311112, 21417312, 21428224, 21434112, 21624192, 21711312, 21721392, 21744128, 21866112, 22137192, 22192128, 22194432, 22211136, 22233312, 22281216, 23126112, 23342112, 23421312, 23491296, 24112128, 26142912, 27232128, 27482112, 27621216, 28212224, 28221312, 28221696, 28422144.

Some larger examples :