A295768 Triangular numbers that can be represented as a sum of two distinct triangular numbers, and as a product of two triangular numbers greater than 1.

990, 1540, 2850, 4851, 8778, 11781, 15400, 26796, 43956, 61425, 61776, 70125, 105570, 145530, 176715, 189420, 270480, 303810, 349866, 437580, 526851, 715806, 719400, 749700, 799480, 810901, 828828, 1037520, 1050525, 1185030, 1493856, 1788886, 1921780, 2001000

Offset: 1

Author

Alex Ratushnyak, Nov 27 2017

Keywords

• nonn

Comments

Intersection of A188630 and A260647.

Examples

			990 is representable as a product of two triangular numbers, 990 = 660 * 15, and as a sum, 990 = 780 + 210, therefore 990 is in the sequence.
		

Crossrefs

Cf. A000217, A188630, A260647.

Programs

Mathematica

maxTerm = 3*10^6; imax = Ceiling[(Sqrt[8*maxTerm + 1] - 1)/2];
TriangularQ[n_] := IntegerQ[Sqrt[8n + 1]];
t[op_] := Table[If[1 < i < j, op[i*(i + 1)/2 , j*(j + 1)/2], Nothing], {i, 2, imax}, {j, i + 1, imax}] // Flatten // Select[#, # <= maxTerm && TriangularQ[#]&]& // Union;
Intersection[t[Plus], t[Times]] (* Jean-François Alcover, Dec 05 2017 *)