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pentagonal n.  and  tau n.

First numbers that belong to both sets:

1, 12, 376, 852, 1520, 7740, 8400, 14652, 31032, 38320, 98176, 106800, 133952, 185680, 233840, 273280, 345360, 380772, 422676, 497376, 516560, 766480, 836640, 884352, 1203776, 1233520, 1322112, 1381920, 1606320, 1881040, 1918176, 2246652, 2257680, 2456960, 2581360, 2624832, 2708832, 2753360, 3109680, 3157376, 3442080, 4112676, 4152512, 4369920, 4478112, 4645520, 4816000, 5408352, 5714480, 5779072, 6488560, 6538572, 6557376, 7741840, 7816992, 7961472, 8037680, 8638800, 9187200, 9343776, 9426320, 10076400, 10836672, 11096240, 11893376, 11986480, 12440160, 12718160, 13096560, 13310172, 13381760, 13860880, 14154240, 14553280, 14628132, 14853840, 15667120, 15744780, 15978912, 16611712, 16932720, 17175492, 17450676, 17914176, 18362752, 18923280, 19384240, 19438200, 19960032, 21148160, 21510160, 21840876, 21875232, 22116480, 22614592, 24130176, 24383520, 25299120, 26495712, 27066132, 27991440, 28407680, 29249376, 29289132, 29395280, 30103360, 30534960, 30684032, 31119760, 32292080, 33798640, 35019920, 35485312, 36115520, 36899920, 37063776, 38024320, 38509200, 39319040, 40479440, 41309632, 41435676, 43011360, 43349376, 43526960, 44911440, 45620080, 46151040, 46501152, 46551276, 48851920, 49401312, 50318000, 51067920, 51999872, 53136480, 54484080, 55064192, 56031760, 56822960, 58403280, 60214176, 64547120, 64763776, 66670000, 67311552, 68380880, 69254640, 70998160, 71225376, 75016240, 75249792, 75696672, 75931280, 77756400, 80084720, 81958800, 82491876, 82669952, 82915120, 83093652, 83630400, 84101472, 84821840, 87986592, 89208560, 92948640, 94466176, 94728240, 96765520, 97538112, 99287676, 99947772, 102238176, 104629680, 105709840, 107048832, 107861360, 108141376, 111426432, 111970080, 116446176, 117001920, 118997520, 120417920, 125058176, 125414532, 126817440, 127701680, 128588992, 131269360, 133665680, 134204292, 134573440, 136713040, 137631072, 139158320, 139476352, 140403600, 143820000, 145706176, 148558480, 148887072, 149515392, 149845040, 152404560, 155657360, 158265840, 158604992, 159593680, 160585440, 169298752, 169649520, 170672000, 172372240, 172629612, 178602160, 179651232, 181758592, 182816880, 183181376, 185309280, 187449472, 191664972, 192479712, 193568720, 199059840, 201660240, 202495932, 203508032, 204627760, 205013376, 205750560, 211802592, 212944880, 214090240, 215994000, 217147520, 218702400, 219863120, 223363712, 224536720, 226486272, 231229376, 234818960, 239648080, 240065376, 242500480, 246983920, 247407552, 255682176, 262423680, 263257632, 264530960, 268810960, 270943680, 272235440, 273003876, 276129152, 278740320, 281815920, 283133312, 284784372, 285322000, 285777312, 286647552, 287103920, 289641276, 290642640, 293783040, 294665376, 297362560, 298715760, 300538960, 302793792, 304159280, 304629376, 308747440, 314281200, 318463776.

Some larger examples :