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pernicious n.  and  Ruth-Aaron pair

First numbers that belong to both sets:

5, 6, 9, 24, 25, 49, 50, 104, 369, 370, 493, 714, 949, 1330, 1521, 1682, 1863, 2108, 2300, 2492, 2601, 2784, 3248, 4185, 4186, 4191, 4192, 5405, 5406, 5560, 6556, 6812, 6868, 8281, 8464, 8855, 8856, 9800, 12352, 13776, 16933, 17081, 18491, 18656, 21184, 24880, 25840, 26642, 28448, 33020, 35457, 37828, 40081, 40082, 41261, 41262, 42624, 43681, 44831, 44832, 44891, 48762, 49240, 57076, 61761, 63345, 63427, 64233, 68265, 70356, 75141, 89979, 98645, 109939, 110608, 128775, 141341, 141489, 143623, 154843, 155708, 174096, 180359, 180360, 204259, 215391, 215392, 224105, 224257, 231285, 235586, 244595, 250995, 261020, 261568, 263628, 265112, 268191, 268192, 268656, 289316, 292455, 296752, 319428, 329988, 332994, 333801, 333802, 346692, 351075, 361064, 370349, 380439, 380964, 384312, 388450, 394856, 417163, 421820, 430604, 437716, 441212, 453474, 457899, 461824, 470119, 477093, 509851, 525225, 529194, 540281, 550033, 554682, 560150, 563391, 564924, 565824, 576985, 583463, 587264, 618751, 624079, 639847, 665323, 667629, 671019, 685229, 693611, 694431, 732088, 740727, 742509, 742853, 742854, 748230, 767833, 773605, 801296, 823151, 838935, 839375, 844864, 849376, 850746, 861399, 869054, 878899, 882926, 890127, 890724, 901747, 906019, 909625, 911075, 911537, 911538, 917864, 944108, 956039, 959581, 959582, 962141, 976376, 977778, 977896, 999072, 1023641, 1039888, 1045951, 1054828, 1062874, 1100281, 1131812, 1166068, 1172948, 1173148, 1173505, 1191133, 1193984, 1199988, 1232747, 1243501, 1252096, 1252509, 1252510, 1261008, 1263679, 1275547, 1275731, 1293139, 1302093, 1306247, 1306248, 1315977, 1329129, 1329130, 1330407, 1330448, 1351273, 1361071, 1386536, 1386903, 1428857, 1428858, 1431213, 1459863, 1477311, 1492032, 1496550, 1496781, 1497465, 1497466, 1512411, 1516788, 1517450, 1549454, 1550855, 1572176, 1600963, 1609736, 1618789, 1647100, 1744920, 1754463, 1762124, 1773134, 1777027, 1799940, 1806367, 1806368, 1806949, 1806950, 1809709, 1809710, 1858645, 1864056, 1903983, 1915577, 1915578, 1926236, 1939625, 1939626, 1943404, 1945048, 1958320, 1962796, 2003631, 2009351, 2020800, 2022344, 2024867, 2040752, 2041585, 2041586, 2042950, 2045977, 2048935, 2049318, 2065122, 2067890.

Some larger examples :