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decagonal n.  and  sphenic n.

First numbers that belong to both sets:

370, 742, 1105, 2626, 4795, 5365, 5662, 6601, 8326, 8695, 11077, 13282, 16705, 17755, 21682, 27307, 28645, 35062, 44626, 52555, 64135, 74665, 76867, 81367, 83665, 95635, 103201, 105787, 109726, 119197, 126202, 127627, 130501, 149962, 154645, 157807, 164227, 169126, 182542, 184255, 194701, 198247, 205435, 209077, 220195, 255277, 257302, 267547, 288637, 292951, 299482, 308302, 315001, 342517, 356707, 361501, 371185, 385951, 416347, 424126, 453265, 464101, 477826, 480595, 486157, 511582, 537655, 549451, 573427, 585607, 629245, 648427, 667897, 687655, 700987, 783667, 790765, 805057, 812251, 848701, 867226, 870955, 878437, 893497, 947215, 962851, 1018585, 1034797, 1055242, 1134757, 1143295, 1226002, 1266187, 1329985, 1371826, 1404817, 1491451, 1501237, 1641601, 1651867, 1682857, 1714135, 1745701, 1815082, 1831285, 1842127, 1896817, 1907851, 1930015, 1946722, 2146957, 2326387, 2344726, 2363137, 2418802, 2437501, 2462545, 2513017, 2576827, 2615497, 2628451, 2654455, 2693701, 2733235, 2813167, 2907877, 2990305, 2997226, 3073885, 3102001, 3137326, 3144415, 3230107, 3273385, 3316951, 3427126, 3449377, 3486622, 3554167, 3584395, 3599557, 3629977, 3675847, 3737455, 3783997, 3925351, 3973045, 3981022, 4045126, 4069297, 4248751, 4398457, 4448935, 4516687, 4602097, 4775317, 4784062, 4810345, 4933951, 4969555, 5023201, 5176762, 5204101, 5295751, 5314177, 5425405, 5462737, 5481451, 5689417, 5737222, 5746807, 5804485, 5881837, 6087322, 6176467, 6276277, 6336547, 6457951, 6519085, 6580507, 6662851, 6766501, 7039735, 7242826, 7275157, 7329202, 7340035, 7426987, 7470655, 7536397, 7757617, 7936897, 7959451, 8004655, 8038642, 8163877, 8209657, 8267062, 8278567, 8440477, 8452102, 8510347, 8580505, 8592226, 8769001, 8911717, 8983507, 9127951, 9164242, 9346777, 9518767, 9592957, 9642577, 9667435, 9717247, 9792205, 9867451, 9968227, 10044145, 10094917, 10120351, 10158562, 10196845, 10248001, 10350697, 10466842, 10583635, 10635751, 10661857, 10740367, 10792867, 10832326, 11057287, 11190697, 11257702, 11351845, 11432851, 11459917, 11704951, 11800942, 11842201, 12174865, 12258751, 12286777, 12300802, 12371047, 12455605, 12682501, 12768115, 12796717, 12882715, 12940207, 12969001, 13113451, 13156942, 13287847, 13507462, 13581067, 13847701, 13907305, 13937155, 14116927, 14177107, 14297851, 14343262, 14358415, 14449501, 14525626, 14724487, 14755201, 14909251, 14940157, 15033067, 15219751, 15376201, 15501937, 15659827, 15754945, 15882217, 15946045.

Some larger examples :