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centered square n.  and  Harshad n.

First numbers that belong to both sets:

1, 5, 481, 20605, 26221, 35113, 82825, 98125, 124501, 225121, 367225, 444625, 721201, 854125, 901825, 920725, 970225, 1543525, 1607425, 1632625, 2207101, 2369665, 2435425, 2515525, 2547025, 3626125, 3762025, 4733965, 5899613, 6326125, 6418945, 6505225, 6774881, 7284745, 8028025, 8706965, 9719641, 9763781, 9843485, 10093525, 10156525, 10319425, 12039325, 12216625, 12465025, 12877813, 13411021, 14542225, 14813125, 15573781, 16479541, 17070325, 17152225, 17481785, 18855941, 18966641, 19052965, 20116825, 20396885, 21998345, 22734025, 23072425, 23385961, 25539805, 25611325, 26230525, 27298661, 29946061, 32877941, 33154225, 35946721, 36611125, 36988601, 39046285, 39702961, 40113925, 40437025, 40563025, 43776725, 47404585, 48127861, 50772965, 52459525, 53117125, 54007225, 55851881, 63202525, 63360025, 66735905, 66990313, 68855113, 69726241, 69820745, 74017945, 75755741, 76892401, 77812813, 82342945, 83295325, 84877421, 85373245, 86342941, 88351925, 91030525, 94765145, 95316625, 98182085, 98434481, 103061725, 104733865, 105458765, 110157325, 110365225, 110900725, 114594661, 115201021, 117152125, 119954561, 123921025, 124141525, 124899013, 127696181, 130524325, 131106625, 131333425, 131657765, 135646921, 135976541, 139762481, 142855705, 152687813, 154124125, 154334881, 156698105, 157158721, 158473405, 162126025, 164910961, 166257613, 169188013, 170072125, 170330425, 170551981, 174601985, 174938513, 178623901, 179229245, 181660861, 188665313, 191433745, 193828361, 196039801, 198343445, 203112013, 204161425, 204687145, 205173025, 207937225, 209449045, 213686465, 215136025, 223513225, 223597805, 223978613, 232352125, 233431225, 237598201, 239476613, 239870705, 242022001, 242154025, 244050325, 244890581, 245466325, 247108681, 250678441, 260444665, 261495581, 261907385, 265812625, 267521581, 272868161, 273288821, 278645225, 281390365, 283148605, 284482805, 290814845, 294201025, 296339513, 297411661, 306108025, 308438285, 308885513, 309880513, 313876513, 314578445, 326682361, 330065125, 330784921, 333826961, 339744245, 340422325, 346660781, 351310525, 353168465, 361616725, 364311025, 365878301, 365932405, 366365381, 377712613, 379308425, 379804361, 384171481, 386225425, 386614625, 392980613, 393485405, 396239401, 398325313, 400643125, 403081225, 404957341, 413310001, 413942765, 415209745, 417344941, 421573685, 428747045, 434623645, 435449561, 435980921, 436808125, 442323025, 442739525, 443751841, 454300225, 458045645, 461563345, 463814425, 464972513, 465521585, 474782113, 477065161, 480097085, 484320565, 487750145, 495463721, 516714805, 519096421, 519547613, 524264581, 526663513, 526923185, 527507681, 534939341, 535528265, 543609365, 551750981, 553014025, 559350905, 559953113, 562901905, 567609125, 568215761, 582940513, 584922605, 593366801, 593504605, 601802125, 605902861, 608481613, 616672081, 618429281, 619062485, 631936801, 632150125, 635853461, 636495521.

Some larger examples :