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gapful n.  and  pentagonal n.

First numbers that belong to both sets:

176, 330, 1001, 1080, 1335, 1520, 1717, 1820, 2380, 2625, 2882, 6305, 8400, 11310, 12105, 12650, 13490, 13776, 14652, 14950, 15555, 16485, 17120, 18760, 19780, 20475, 21540, 23375, 23751, 31465, 32340, 42252, 55200, 59900, 75825, 82720, 95130, 101270, 104412, 106800, 109215, 110840, 113300, 115787, 117460, 119145, 121695, 122551, 123410, 124272, 125137, 127750, 130390, 132165, 134850, 135751, 141220, 145860, 148680, 153440, 160230, 162197, 163185, 164176, 165170, 168170, 172212, 173230, 174251, 175275, 178365, 180440, 185680, 188860, 190995, 194220, 197472, 214137, 224460, 230300, 233840, 239800, 259376, 260625, 270725, 273280, 279720, 283620, 290180, 291501, 292825, 295482, 300832, 319935, 329707, 345360, 354051, 359905, 362850, 367290, 370265, 377755, 385320, 408465, 425867, 461760, 470120, 525400, 539700, 548735, 583752, 608335, 633425, 677040, 683100, 720027, 734650, 749420, 760060, 770775, 801176, 814385, 836640, 877455, 940500, 1005732, 1008190, 1013115, 1020525, 1025480, 1037920, 1040417, 1045420, 1050435, 1057980, 1065552, 1075690, 1088430, 1096110, 1108970, 1119312, 1127100, 1134915, 1140140, 1142757, 1148000, 1161160, 1166445, 1174395, 1179710, 1182372, 1193050, 1201090, 1203776, 1206465, 1214550, 1230801, 1233520, 1247160, 1255380, 1263627, 1269140, 1288530, 1296885, 1302470, 1310870, 1322112, 1324930, 1330575, 1339065, 1341901, 1344740, 1358980, 1367560, 1373295, 1376167, 1381920, 1384801, 1390572, 1402150, 1407957, 1413776, 1416690, 1425450, 1440110, 1451892, 1460760, 1469655, 1475600, 1484540, 1499500, 1502501, 1505505, 1514535, 1520570, 1523592, 1526617, 1535710, 1544830, 1550925, 1560090, 1581580, 1597020, 1606320, 1621880, 1643790, 1653225, 1659530, 1665847, 1669010, 1672176, 1681692, 1684870, 1691235, 1700805, 1707200, 1723240, 1732900, 1739355, 1749060, 1758792, 1771810, 1788150, 1794707, 1797990, 1814450, 1827672, 1837620, 1847595, 1854260, 1864280, 1881040, 1887765, 1897875, 1901251, 1904630, 1908012, 1918176, 1921570, 1931770, 1938585, 1948830, 1972840, 1990080, 2000460, 2014342, 2017820, 2112860, 2116422, 2130700, 2141440, 2145026, 2155802, 2159400, 2170212, 2221025, 2250325, 2257680, 2272426, 2276120, 2287220, 2305780, 2313225, 2316952, 2343125, 2407300, 2414907, 2426340, 2437800, 2456960, 2460801, 2518776, 2561720, 2581360, 2593180, 2601075, 2612940, 2628802, 2632775, 2700775.

Some larger examples :