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persistent n.  and  powerful n.

First numbers that belong to both sets:

1324890675, 1532487609, 1854207963, 2081549376, 3042571896, 3047618592, 3285697041, 3719048256, 3827401956, 4081962375, 4163098752, 5102673489, 5397840216, 7025391648, 7041963825, 7654803912, 8503421796, 8967143025, 9761835204, 9876523104, 10208475369, 10259816437, 10347568729, 10456893728, 10694823752, 10876945032, 13529467008, 13592047688, 14731890625, 15072963984, 15409839627, 15879045632, 16203507849, 16273958400, 17028534096, 17054792836, 17250983649, 17760359824, 19023581476, 20348590176, 20948530176, 21309946875, 23017895064, 23089156475, 23816094752, 25061739481, 25647381904, 26397150784, 27184095376, 27304918564, 27404815936, 27538074916, 27735904681, 28170039456, 28374054916, 29456170384, 30198740625, 30264517089, 30421987561, 30517294864, 31040528967, 31528974096, 31876459200, 31948702564, 34900217856, 35804961792, 37154289608, 37259481600, 39152714608, 39784690521, 40396578121, 40597681352, 41039265748, 41753200896, 41859703296, 42357961800, 43250860197, 44739018256, 45108237769, 45192807396, 46159372800, 47031295689, 47358029161, 48618350792, 49307968512, 49370618025, 49736925108, 49918730625, 50439961728, 50994127368, 51846379204, 52381476900, 53416298907, 54078396192, 54510736928, 54607193288, 54637082819, 54703128769, 58297136704, 59362175048, 60352747819, 61853479200, 63402859917, 67293548100, 67535804912, 68135094729, 69421087953, 69713425089, 69743528100, 70152938496, 71465328900, 71503829604, 72145290368, 72460153928, 74902931856, 75318960249, 75461738209, 76415203489, 81195362704, 81639247500, 84416397025, 87965034921, 89478036512, 90271359468, 91302478569, 91352476800, 91625473809, 91752044836, 94618375201, 95371027684, 96438197025, 97503981624, 97940123568, 98175243600.