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amenable n.  and  Ruth-Aaron pair

First numbers that belong to both sets:

5, 8, 9, 16, 24, 25, 49, 77, 104, 105, 125, 153, 369, 492, 493, 948, 949, 1520, 1521, 2108, 2300, 2492, 2600, 2601, 2784, 3248, 3249, 4185, 4192, 5405, 5560, 5561, 5960, 6556, 6557, 6812, 6868, 8280, 8281, 8464, 8856, 9800, 9801, 10648, 12352, 13776, 14588, 16932, 16933, 17080, 17081, 18656, 21184, 24024, 24025, 24432, 24433, 24880, 24881, 24896, 25840, 26649, 28448, 28449, 28809, 33020, 35456, 35457, 37828, 37829, 37881, 40081, 41261, 42624, 42625, 43216, 43680, 43681, 44832, 44892, 47544, 47545, 48204, 49240, 49241, 53192, 53193, 57076, 61760, 61761, 63344, 63345, 63665, 64232, 64233, 68264, 68265, 68949, 70356, 70357, 72500, 72501, 75140, 75141, 81176, 89980, 95709, 98120, 98644, 98645, 99164, 106800, 106893, 109940, 110608, 112080, 113284, 118656, 118657, 132209, 141340, 141341, 141488, 141489, 148216, 155112, 155708, 155709, 172773, 174096, 174097, 180360, 189080, 189081, 197657, 208581, 215392, 216293, 224104, 224105, 224256, 224257, 228600, 230124, 230125, 231284, 231285, 244036, 244596, 244853, 247456, 248109, 250996, 261020, 261568, 261569, 263328, 263628, 263629, 265112, 265113, 268192, 268656, 268657, 268716, 278277, 289316, 289317, 294336, 296112, 296752, 304325, 319428, 319429, 329988, 329989, 333801, 346692, 346693, 350600, 351076, 361064, 370348, 370349, 373704, 380964, 381728, 381729, 384312, 384313, 394856, 404973, 407836, 416120, 417164, 421820, 430604, 430605, 436932, 436933, 437716, 441212, 445305, 457900, 461824, 461825, 466773, 470120, 477092, 477093, 488976, 488977, 508564, 509852, 525224, 525225, 537916, 537917, 540280, 540281, 547525, 550032, 550033, 557536, 564924, 564925, 565824, 571040, 572016, 576984, 576985, 587264, 587265, 598249, 608316, 608317, 618752, 624080, 639848, 643468, 667628, 667629, 671020, 685228, 685229, 696436, 696437, 732088, 732089, 732200, 742508, 742509, 742853, 767832, 767833, 773312, 773313, 773604, 773605, 801296, 820600, 820601, 821272, 827896, 838936, 839200, 839376, 842128, 844864, 844865, 849376, 851709, 856608, 859408, 859409, 861400, 890724, 901748, 906020, 909624.

Some larger examples :