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amenable n.  and  centered pentagonal n.

First numbers that belong to both sets:

1, 16, 76, 141, 181, 276, 456, 601, 681, 856, 1156, 1381, 1501, 1756, 2176, 2481, 2641, 2976, 3516, 3901, 4101, 4516, 5176, 5641, 5881, 6376, 7156, 7701, 7981, 8556, 9456, 10081, 10401, 11056, 12076, 12781, 13141, 13876, 15016, 15801, 16201, 17016, 18276, 19141, 19581, 20476, 21856, 22801, 23281, 24256, 25756, 26781, 27301, 28356, 29976, 31081, 31641, 32776, 34516, 35701, 36301, 37516, 39376, 40641, 41281, 42576, 44556, 45901, 46581, 47956, 50056, 51481, 52201, 53656, 55876, 57381, 58141, 59676, 62016, 63601, 64401, 66016, 68476, 70141, 70981, 72676, 75256, 77001, 77881, 79656, 82356, 84181, 85101, 86956, 89776, 91681, 92641, 94576, 97516, 99501, 100501, 102516, 105576, 107641, 108681, 110776, 113956, 116101, 117181, 119356, 122656, 124881, 126001, 128256, 131676, 133981, 135141, 137476, 141016, 143401, 144601, 147016, 150676, 153141, 154381, 156876, 160656, 163201, 164481, 167056, 170956, 173581, 174901, 177556, 181576, 184281, 185641, 188376, 192516, 195301, 196701, 199516, 203776, 206641, 208081, 210976, 215356, 218301, 219781, 222756, 227256, 230281, 231801, 234856, 239476, 242581, 244141, 247276, 252016, 255201, 256801, 260016, 264876, 268141, 269781, 273076, 278056, 281401, 283081, 286456, 291556, 294981, 296701, 300156, 305376, 308881, 310641, 314176, 319516, 323101, 324901, 328516, 333976, 337641, 339481, 343176, 348756, 352501, 354381, 358156, 363856, 367681, 369601, 373456, 379276, 383181, 385141, 389076, 395016, 399001, 401001, 405016, 411076, 415141, 417181, 421276, 427456, 431601, 433681, 437856, 444156, 448381, 450501, 454756, 461176, 465481, 467641, 471976, 478516, 482901, 485101, 489516, 496176, 500641, 502881, 507376, 514156, 518701, 520981, 525556, 532456, 537081, 539401, 544056, 551076, 555781, 558141, 562876, 570016, 574801, 577201, 582016, 589276, 594141, 596581, 601476, 608856, 613801, 616281, 621256, 628756, 633781, 636301, 641356, 648976, 654081, 656641, 661776, 669516, 674701, 677301, 682516, 690376, 695641, 698281, 703576, 711556, 716901, 719581, 724956, 733056, 738481, 741201, 746656, 754876, 760381, 763141, 768676, 777016, 782601.

Some larger examples :