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centered octagonal n.  and  Harshad n.

First numbers that belong to both sets:

1, 9, 81, 225, 441, 1521, 2025, 2401, 2601, 3969, 4225, 11025, 12321, 13689, 40401, 42849, 59049, 62001, 75625, 77841, 88209, 99225, 103041, 104329, 110889, 123201, 194481, 198025, 227529, 251001, 263169, 281961, 286225, 297025, 301401, 321489, 363609, 385641, 390625, 431649, 442225, 455625, 480249, 508369, 525625, 558009, 585225, 613089, 648025, 664225, 670761, 700569, 762129, 819025, 826281, 893025, 962361, 970225, 990025, 998001, 1010025, 1014049, 1022121, 1034289, 1092025, 1108809, 1155625, 1177225, 1185921, 1212201, 1221025, 1225449, 1265625, 1306449, 1320201, 1347921, 1357225, 1380625, 1432809, 1476225, 1520289, 1575025, 1750329, 1809025, 1836025, 1946025, 2047761, 2059225, 2088025, 2099601, 2152089, 2259009, 2325625, 2356225, 2368521, 2424249, 2480625, 2595321, 2608225, 2640625, 2653641, 2712609, 2772225, 2893401, 2907025, 2941225, 3017169, 3101121, 3143529, 3207681, 3258025, 3272481, 3538161, 3553225, 3591025, 3744225, 3814209, 3900625, 3940225, 3956121, 4004001, 4028049, 4247721, 4264225, 4305625, 4313929, 4473225, 4626801, 4644025, 4704561, 4862025, 5085025, 5267025, 5433561, 5452225, 5517801, 5697769, 5861241, 6125625, 6215049, 6325225, 6765201, 6943225, 7049025, 7241481, 7263025, 7317025, 7535025, 7812025, 7834401, 8037225, 8242641, 8323225, 8346321, 8673025, 9090225, 9308601, 9333025, 9641025, 9878449, 9966649, 10093329, 10195249, 10310521, 10323369, 10439361, 10465225, 10791225, 10843849, 11055625, 11148921, 11336689, 11390625, 11512449, 11634921, 11662225, 11730625, 11758041, 12131289, 12285025, 12355225, 12383361, 12510369, 12638025, 12924025, 13024881, 13155129, 13286025, 13653025, 13682601, 13950225, 14010049, 14085009, 14250625, 14326225, 14356521, 14630625, 14907321, 15015625, 15046641, 15327225, 15642025, 15673681, 15721225, 16265089, 16362025, 16443025, 16491721, 17065161, 17181025, 17514225, 18122049, 18740241, 18861649, 19053225, 19404025, 19509889, 20007729, 20169081, 20295025, 20657025, 21483225, 21650409, 21818241, 22325625, 22667121, 22705225, 22800625, 23184225, 23571025, 23707161, 24000201, 24059025, 24413481, 24453025, 24552025, 24950025, 25010001, 25130169, 25310961, 25351225, 25452025, 25492401, 26040609, 26122321, 26183689, 26224641, 26409321, 26512201, 26759929, 26801329, 27154521, 27300625, 27342441, 27531009, 27720225, 28143025, 28783225, 28998225, 29106025, 29214025, 29430625, 29975625, 30085225, 30151081, 30195025, 30636225, 31080625, 31192225, 31236921, 31640625, 32046921, 32092225, 32205625, 32661225, 32890225, 33235225, 33281361, 34117281, 34164025.

Some larger examples :