A295768 - OEIS

%I #9 Dec 26 2017 18:28:13

%S 990,1540,2850,4851,8778,11781,15400,26796,43956,61425,61776,70125,

%T 105570,145530,176715,189420,270480,303810,349866,437580,526851,

%U 715806,719400,749700,799480,810901,828828,1037520,1050525,1185030,1493856,1788886,1921780,2001000

%N 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.

%C Intersection of A188630 and A260647.

%e 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.

%t maxTerm = 3*10^6; imax = Ceiling[(Sqrt[8*maxTerm + 1] - 1)/2];

%t TriangularQ[n_] := IntegerQ[Sqrt[8n + 1]];

%t 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;

%t Intersection[t[Plus], t[Times]] (* _Jean-François Alcover_, Dec 05 2017 *)

%Y Cf. A000217, A188630, A260647.

%K nonn

%O 1,1

%A _Alex Ratushnyak_, Nov 27 2017