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amenable n.  and  repunit

First numbers that belong to both sets:

13, 21, 40, 57, 73, 85, 121, 133, 156, 157, 241, 273, 341, 364, 381, 400, 421, 553, 585, 601, 757, 781, 813, 820, 993, 1057, 1093, 1261, 1333, 1365, 1464, 1561, 1641, 1885, 1893, 1981, 2257, 2353, 2380, 2653, 2757, 2801, 3081, 3193, 3280, 3541, 3616, 3661, 4033, 4161, 4369, 4557, 4681, 4693, 5113, 5220, 5257, 5461, 5701, 5853, 6321, 6481, 6973, 7141, 7240, 7381, 7657, 7833, 8373, 8421, 8557, 9121, 9313, 9724, 9841, 9901, 10101, 10713, 10921, 11557, 11773, 12433, 12657, 12720, 13341, 13573, 14281, 14425, 14521, 15253, 15501, 16105, 16257, 16276, 16513, 17293, 17557, 18361, 18633, 19461, 19608, 19741, 20440, 20593, 20881, 21757, 21845, 22053, 22621, 22765, 22953, 23257, 24181, 24493, 25260, 25441, 25761, 26733, 27061, 28057, 28393, 29413, 29524, 29757, 30784, 30801, 30941, 31153, 32221, 32581, 33673, 33825, 34041, 35157, 35533, 36673, 37057, 37060, 37449, 38221, 38613, 39801, 40201, 41413, 41821, 43057, 43473, 44136, 44733, 45157, 46441, 46873, 47989, 48181, 48621, 49953, 50401, 51757, 52060, 52213, 53593, 54057, 54241, 55461, 55933, 57361, 57841, 59293, 59781, 60880, 61257, 61753, 63253, 63757, 65281, 65641, 65793, 67341, 67861, 69433, 69905, 69961, 70644, 71557, 72093, 73713, 74257, 75901, 76453, 78121, 78681, 80373, 80941, 81400, 82657, 83233, 84973, 85557, 87165, 87321, 87381, 87913, 88573, 88741, 89701, 90301, 92113, 92721, 93196, 94557, 95173, 97033, 97656, 97657, 99541, 100173, 102081, 102721, 104653, 105301, 106080, 107257, 107913, 109893, 110557, 112561, 112945, 113233, 115261, 115941, 117993, 118681, 120100, 120757, 121453, 123553, 124257, 126381, 127093, 129241, 129961, 132133, 132861, 135057, 135304, 135793, 137257, 137561, 138013, 138757, 141001, 141753, 143365, 144021, 144781, 147073, 147841, 150157, 150933, 151740, 153273, 154057, 156421, 157213, 159601, 160401, 162813, 163621, 166057, 166873, 168421, 169333, 169456, 170157, 172641, 173473, 175981, 176821, 177156, 178809.

Some larger examples :