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centered square n.  and  Smith n.

First numbers that belong to both sets:

85, 265, 2965, 5305, 6385, 30505, 48361, 60205, 91165, 129541, 138865, 295681, 317605, 338665, 368941, 384565, 416785, 425965, 588613, 608305, 733261, 810265, 856741, 893785, 918013, 953581, 1081921, 1218361, 1795513, 1950313, 2006005, 2245081, 2360965, 2479765, 2502085, 2583265, 3052921, 3572465, 3583165, 3609985, 3680185, 3707365, 3756541, 4236961, 4617761, 4889065, 5002285, 5148841, 5501245, 5681821, 5708821, 5865313, 5892745, 5954701, 6397465, 6592081, 7095145, 7261861, 7330621, 7399705, 7538845, 7647961, 7749985, 8327281, 8623705, 8967613, 9544081, 10228765, 10639885, 11059105, 11698285, 12315685, 12365365, 13976185, 14900341, 15395701, 17187385, 17351941, 17458141, 17505445, 17671513, 17719105, 17826421, 18210613, 22626265, 22693585, 24227761, 25183705, 25956013, 26013685, 26477365, 26739985, 28478605, 28948441, 30271981, 30552745, 31976005, 32699785, 32991565, 34869601, 35070313, 36902641, 37281613, 39738613, 40617085, 41195965, 42679561, 42883061, 43926565, 44698513, 46590205, 46841521, 47638561, 47736221, 49770265, 50030005, 52132261, 53426785, 54632605, 54737185, 54820921, 58460485, 59350513, 59437705, 62529745, 62932981, 64968601, 67663345, 68925541, 69019501, 69773485, 70080961, 70507813, 71796145, 74627545, 75854245, 76619821, 78187513, 78412765, 78638341, 78864241, 80810185, 82522705, 83346961, 83916013, 84851365, 84981685, 85320985, 86395513, 88059721, 88165921, 88192481, 88405105, 89498821, 89739805, 90357125, 90949585, 91435765, 93639613, 96230065, 97482685.