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Harshad n.  and  Poulet n.

First numbers that belong to both sets:

645, 1387, 1729, 1905, 2465, 2821, 8911, 30121, 126217, 204001, 223345, 272251, 276013, 334153, 488881, 757945, 915981, 934021, 1024651, 1306801, 1398101, 1746289, 2113921, 2719981, 2899801, 4069297, 4504501, 4917781, 5031181, 5034601, 5758273, 5859031, 6973057, 8640661, 8656705, 8719309, 8992201, 10226161, 10974385, 11034365, 11473885, 12261061, 12490201, 12783811, 12945745, 15248773, 17450569, 22066201, 22269745, 22885129, 24158641, 24776557, 25266745, 26921089, 27128201, 27336673, 27401401, 27714961, 28449961, 29593159, 32756581, 33018985, 33848311, 34111441, 35932441, 36765901, 36852481, 38637361, 40886241, 41341321, 42689305, 44963029, 45593065, 47734141, 50176477, 50193793, 53728921, 53795521, 55035001, 57561085, 58903741, 64567405, 64685545, 65523781, 67371265, 67541761, 68958681, 70561921, 75501793, 78120001, 81189433, 81680941, 83099521, 98124481, 102940993, 105309289, 106169761, 107714881, 111837181, 115196033, 119532385, 123718861, 129812761, 134188381, 135556345, 136625941, 139592101, 140167729, 145856701, 148087801, 151833561, 158845569, 159420457, 161293249, 161913961, 164391481, 172596601, 173928601, 176659201, 181449073, 186782401, 188082301, 191752093, 192081097, 192920161, 193708801, 194120389, 200453401, 206623873, 213111163, 233812657, 241031701, 245956501, 247095361, 250200721, 282049705, 289109941, 292236841, 292244833, 294911401, 295308433, 297411661, 303532201, 311388337, 321197185, 328190185, 337420945, 348140881, 364637701, 366069601, 369372193, 370851481, 373241089, 384046273, 395136505, 396539101, 398661901, 417924361, 420468481, 434932961, 469832401, 470122777, 476470401, 496803553, 512096761, 523842337, 527761081, 533860309, 555726421, 557160241, 568227241, 569708161, 600926509, 606682081, 617984101, 639925441, 654947101, 664384321, 677451241, 686129221, 698548201, 710408917, 713588401, 717164449, 730925713, 756249901, 771350581, 786262321, 816075457, 834147721, 834720601, 843704401, 852729121, 867800701, 874017145, 881186801, 886002481, 893601541, 917704081, 952282801, 967714021, 975303121, 1007608753, 1030401901, 1069731901, 1074363265, 1100674561, 1106410033, 1110293101, 1115335585, 1119075841, 1120258657, 1134010801, 1153366501, 1172800729, 1190790721, 1195400641, 1227023785, 1231869601, 1242958501, 1246588201, 1251295501, 1271632465, 1276614145, 1285445305, 1309531861, 1310486905, 1313596201, 1316958721, 1342185841, 1343872153, 1384157161, 1410833281, 1445084173, 1477140085, 1481619601, 1485162721, 1506674521, 1512164841, 1519801381, 1571503801, 1583347105, 1584443341, 1613347741, 1615335085, 1620653761, 1622809111, 1623368293, 1627733341, 1689411601, 1760460481, 1769031901, 1785507361, 1801635265, 1807352209, 1836304561, 1849811041, 1872058105, 1878156001, 1904833393, 1918052065, 1928482601, 1932608161, 1950483601, 1958102641, 1987020361, 1992841201, 2026574201, 2048751901, 2049204781, 2051369281, 2057516461, 2111416021, 2111732857, 2123334577, 2151835381, 2217605545, 2223876601, 2270483281, 2280284137.

Some larger examples :