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d-powerful n.  and  nialpdrome

First numbers that belong to both sets:

1, 2, 3, 4, 5, 6, 7, 8, 9, 43, 63, 332, 333, 994, 4332, 4443, 5320, 5321, 5322, 5432, 6443, 7432, 7632, 8200, 8443, 8864, 9654, 9963, 33220, 33221, 33222, 44332, 53222, 53332, 63320, 63321, 63322, 64332, 64333, 65322, 65433, 66443, 66532, 74322, 75222, 75532, 76432, 85432, 85433, 86554, 86665, 87632, 96522, 96542, 96543, 97443, 97733, 98322, 98542, 98654, 98744, 98764, 98874, 99843, 332222, 433222, 433333, 444443, 522210, 522211, 532220, 532221, 532222, 533322, 543222, 543330, 543331, 543332, 543333, 544322, 544432, 544433, 552222, 553322, 554222, 554332, 643322, 653333, 654432, 654433, 655222, 655422, 663322, 664332, 664422, 666332, 666333, 666443, 666532, 753322, 766322, 773300, 774332, 774333, 776442, 777322, 777542, 844332, 853332, 855222, 855332, 863322, 864332, 865322, 866532, 873332, 875332, 875532, 876432, 876543, 877222, 877733, 877752, 886332, 887433, 964322, 974332, 974442, 974443, 975432, 976332, 977322, 977432, 977540, 977541, 977542, 977543, 977544, 977655, 987532, 997522, 4332220, 4332221, 4332222, 4444332, 5322222, 5444322, 5522222, 5555444, 6433220, 6433221, 6433222, 6443300, 6443322, 6444332, 6444333, 6532222, 6533322, 6543330, 6543331, 6543332, 6543333, 6544322, 6544433, 6554222, 6554332, 6555544, 6643322, 6644332, 6644333, 6653222, 6653332, 6655222, 6655422, 6665543, 6666333, 7433322, 7443220, 7443221, 7443222, 7443332, 7443333, 7444432, 7533222, 7553332, 7554322, 7555333, 7643220, 7643221, 7643222, 7643332, 7644433, 7653322, 7654222, 7655322, 7663220, 7663221, 7663222, 7663333, 7664432, 7733222, 7753222, 7753332, 7754432, 7754433, 7755222, 7755333, 7755422, 7755442, 7755443, 7755532, 7763322, 7764332, 7765320, 7765321, 7765322, 7765432, 7765433, 7776542, 7777643, 8433222, 8443322, 8444330, 8444331, 8444332, 8444333, 8533322, 8543222, 8543332, 8552222, 8553322, 8554222, 8633220, 8633221, 8633222, 8643322, 8653222, 8654432, 8655222, 8655442, 8743332, 8763332, 8766522, 8774332, 8774333, 8776642, 8777320, 8777321, 8777322, 8777743, 8833222, 8855330, 8855331, 8855332, 8855333, 8866443, 8886532, 8887542, 9444322, 9444432, 9522222, 9544222, 9544332, 9632222, 9633322, 9654333, 9654422, 9655322, 9655432, 9664322, 9665422, 9665532, 9733222, 9733332, 9744330, 9744331, 9744332, 9744333, 9753332, 9754322.

Some larger examples :