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Lehmer n.  and  triangular n.

First numbers that belong to both sets:

15, 91, 435, 561, 595, 703, 1891, 2701, 3655, 5151, 8911, 10585, 12403, 15051, 16471, 18721, 26335, 38503, 41041, 49141, 69751, 79003, 88831, 93961, 104653, 115921, 129795, 146611, 157641, 159895, 188191, 218791, 226801, 229503, 269011, 286903, 314821, 334153, 364231, 385003, 485605, 497503, 521731, 534061, 568711, 597871, 651511, 665281, 697971, 721801, 736291, 765703, 795691, 826255, 873181, 915981, 954271, 1004653, 1056331, 1314631, 1373653, 1537381, 1755001, 1869211, 1987021, 2035153, 2233441, 2284453, 2467531, 2521135, 2602621, 2630071, 2741311, 2912491, 3059101, 3178981, 3270403, 3363121, 3449251, 3627471, 3649051, 3812941, 3913003, 3938221, 4014361, 4082653, 4255903, 4504501, 4686391, 4797253, 4909411, 5176153, 5214835, 5292631, 5489641, 5556111, 5690251, 5744355, 5894461, 5977153, 6186403, 6228685, 6313681, 6969511, 7195321, 8086231, 8134561, 8231653, 8378371, 8576011, 8725753, 9080191, 9131401, 9493903, 9863461, 10185841, 10403641, 10679131, 10958221, 11817091, 12169711, 12890503, 13012651, 13073941, 13694761, 14652991, 14783203, 14892153, 14913991, 15243481, 15576571, 15913261, 15981031, 16253551, 16322041, 16666651, 18225703, 18443701, 18736381, 18809911, 19328653, 19703503, 20081953, 20234341, 20310751, 21134751, 21474181, 21789901, 22028203, 22187791, 22670011, 22892761, 22994371, 23567545, 24482503, 24735061, 24904153, 25073821, 25158871, 25500511, 25758253, 26017291, 26714395, 26890111, 27331921, 27509653, 27777331, 27956503, 28406953, 28678951, 30058381, 30525391, 30996001, 31470211, 32332861, 32429431, 32817151, 32914441, 33796531, 33928203, 34391071, 34590403, 34890481, 35292601, 35798491, 35967921, 36307981, 37649503, 37962541, 38171953, 38909431, 39547171, 40621591, 41710411, 42149971, 42702661, 42998901, 43036003, 46094401, 46672291, 47253781, 48191653, 49019851, 49735351, 49975003, 51425011, 52157791, 53060451, 53390611, 53638903, 54637831, 55266841, 57561085, 58725703, 58986091, 59639581, 60033403, 60957361, 61754941, 62289541, 62423551, 63365653, 63907165, 64042903, 64450981, 66096253, 67065571, 67204621, 67902031, 68182003, 68462551, 70015861, 72884701, 73902403, 74927161, 75663451, 76997845, 77146831, 77295961, 77594653, 78644611, 78795181, 79398901, 80918281, 81376903, 81491761, 82452061, 82606231, 83224351, 84116935, 85719871, 87298291, 89532271, 90014653, 90713715, 92936161, 93591721, 93755971, 94414411, 96904081, 97071211, 97741171, 99257005, 101980621, 102839311, 104220703, 106485121, 108067051, 108596953, 109838431, 110016361, 112702591, 113605201, 114329881, 115238971, 116151661, 116701003, 117251641, 117987841, 118172251.

Some larger examples :