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Ruth-Aaron pair  and  sphenic n.

First numbers that belong to both sets:

78, 105, 154, 370, 715, 4191, 5405, 12351, 12727, 16933, 17081, 20451, 21183, 24895, 26643, 33019, 35457, 37829, 47545, 48203, 52555, 89979, 95709, 98119, 98645, 109939, 112079, 141341, 143623, 154843, 155111, 173163, 180359, 197657, 204259, 208581, 248109, 261019, 268657, 268715, 296111, 319429, 329989, 346693, 361063, 370349, 373703, 380438, 380963, 384313, 388451, 394855, 417163, 445306, 477093, 509851, 529195, 540281, 550033, 554683, 565823, 572015, 576985, 608317, 618751, 624079, 639847, 671019, 693611, 732089, 732199, 748231, 820601, 839199, 850747, 851709, 859409, 890723, 906019, 911537, 917863, 961573, 962141, 965095, 977281, 977779, 1006549, 1023641, 1045951, 1053599, 1104263, 1131811, 1172947, 1191133, 1191451, 1199987, 1232747, 1243501, 1246933, 1263679, 1267919, 1275731, 1306247, 1330449, 1354053, 1428857, 1492031, 1496551, 1516787, 1549454, 1562093, 1570279, 1618789, 1671333, 1716629, 1806949, 1807906, 1818227, 1838183, 1858645, 1864057, 1915577, 1926235, 1945049, 1962797, 2020801, 2022343, 2042951, 2045977, 2049319, 2065123, 2105237, 2123666, 2128985, 2138929, 2170599, 2238373, 2260589, 2305397, 2314663, 2339047, 2579309, 2660635, 2701669, 2742395, 2802298, 2849043, 2854739, 2892103, 3003469, 3009413, 3013915, 3026019, 3155779, 3165639, 3205915, 3206342, 3223789, 3240385, 3267442, 3400891, 3414889, 3438521, 3457497, 3468319, 3524497, 3561941, 3573467, 3584053, 3594245, 3602833, 3665135, 3678809, 3696379, 3703589, 3743351, 3844279, 3889343, 3944506, 4055619, 4057123, 4086227, 4124537, 4141523, 4187293, 4187659, 4281467, 4285957, 4339369, 4382689, 4462339, 4614731, 4647221, 4832665, 4846993, 4854877, 4913981, 4958989, 5000206, 5142955, 5152757, 5185519, 5195089, 5242031, 5362347, 5384399, 5432719, 5535655, 5686307, 5733847, 5739449, 5800393, 5898299, 5945777, 5957799, 6029173, 6059083, 6126439, 6143469, 6226399, 6287867, 6296777, 6384993, 6445654, 6476147, 6587089, 6649049, 6662999, 6693479, 6701806, 6829073, 6890179, 6897593, 6905999, 6981341, 7036871, 7073113, 7084297, 7094933, 7142969, 7185385, 7331651, 7349887, 7370371, 7387679, 7418413, 7446997, 7478459, 7483199, 7636546, 7690289, 8108057, 8135591, 8166929, 8167753, 8256679, 8407619, 8417471, 8470481, 8471039, 8481985, 8505407, 8541557, 8608669, 8630497, 8700199, 8746897, 8771059, 8800733, 8864701, 8912251, 8967013, 8976851, 9086045, 9098081, 9150389, 9171651, 9200861, 9226379, 9329191.

Some larger examples :