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

1,1

Comments

Intersection of A188630 and A260647.

Links

Table of n, a(n) for n=1..34.

Example

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.

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 *)

Crossrefs

Cf. A000217, A188630, A260647.

Sequence in context: A087702 A224565 A341604 * A255917 A154071 A218133

Adjacent sequences: A295765 A295766 A295767 * A295769 A295770 A295771

Keyword

nonn

Author

Alex Ratushnyak, Nov 27 2017

Status

approved