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A295768
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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.
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0
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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
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OFFSET
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1,1
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COMMENTS
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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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;
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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