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interprime n.  and  super Niven n.

First numbers that belong to both sets:

4, 6, 9, 12, 30, 50, 60, 102, 120, 150, 240, 300, 420, 600, 660, 1020, 1050, 1100, 1140, 1320, 2640, 3000, 3006, 3030, 3120, 3300, 3330, 3600, 4020, 4500, 4800, 5010, 5100, 6060, 6300, 6660, 8200, 9000, 9360, 9990, 10008, 10050, 10140, 10500, 20004, 20080, 20640, 22000, 22020, 28800, 30000, 30300, 30960, 36900, 42600, 48480, 50010, 50040, 50500, 50550, 55050, 60660, 80640, 80880, 82200, 88800, 100140, 100200, 100800, 102000, 102300, 103200, 104000, 104040, 111120, 113400, 121020, 130200, 180000, 200020, 201120, 204120, 204600, 206640, 210120, 214200, 220020, 220800, 226200, 231000, 246000, 282240, 300000, 300300, 301020, 310020, 315000, 320040, 330300, 351000, 363060, 363600, 366300, 393300, 400020, 400400, 400680, 401400, 403200, 404040, 411000, 420000, 422400, 440000, 441000, 444000, 444480, 460200, 488400, 500220, 505050, 513000, 525000, 550200, 600240, 600300, 603900, 630900, 633060, 660000, 660600, 680400, 700770, 707700, 800080, 801000, 880080, 880800, 900090, 909090, 909900, 950040, 990000, 990360, 1000400, 1001010, 1001100, 1003200, 1010000, 1010220, 1012020, 1014000, 1016400, 1023000, 1023120, 1030020, 1035000, 1040040, 1044000, 1053000, 1100040, 1111200, 1112100, 1201020, 1210020, 1210200, 1212120, 1311000, 1400100, 1440000, 1501500, 2000100, 2004000, 2008080, 2008800, 2010120, 2011020, 2011200, 2024400, 2030100, 2040240, 2041200, 2042400, 2060040, 2062200, 2080000, 2110020, 2111100, 2120100, 2220120, 2226000, 2242200, 2242800, 2260200, 2331000, 2600400, 2622000, 3000300, 3003660, 3009600, 3021000, 3069360, 3093300, 3111000, 3150000, 3306600, 3636360, 3663000, 3930300, 4000080, 4000500, 4001100, 4002000, 4004040, 4006800, 4008000, 4040000, 4040880, 4044600, 4084080, 4095000, 4120200, 4140000, 4284000, 4408800, 4410000, 4884000, 5000550, 5002200, 5004000, 5045040, 6000120, 6002040, 6003360, 6006060, 6006600, 6022800, 6033600, 6039000, 6040440, 6066000, 6204000, 6222000, 6330060, 6333300, 6426000, 6600060, 7000000, 7007070, 7035000, 7350000, 8002200, 8008000, 8008800, 8020000, 8040000, 8064000, 8109000, 8208000, 8408400, 8440080, 8480400, 8800080, 8820000, 9900900, 10000140, 10001100, 10001400, 10010220, 10012020, 10035000, 10044000, 10080000, 10100010, 10100220, 10100400, 10110000, 10110240, 10121100, 10210020.

Some larger examples :