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 A174906 a(n) is the index of the first triangular number T_i exceeding T_n such that the product of T_i*T_n is a perfect square. 0
 24, 48, 80, 120, 168, 224, 49, 360, 440, 528, 624, 728, 840, 960, 1088, 1224, 1368, 1520, 1680, 1848, 2024, 2208, 242, 2600, 2808, 3024, 3248, 3480, 3720, 3968, 4224, 4488, 4760, 5040, 5328, 5624, 5928, 6240, 6560, 6888, 7224, 7568, 7920, 8280, 8648 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS "You can find an infinite number of [different] triangular numbers such that when multipled together form a square number. For example, for every triangular number, T_n, there are an infinite number of other triangular numbers, T_m, such that T_n*T_m is a square. For example, T_2 * T_24 = 30^2." REFERENCES Clifford A. Pickover, The Loom of God, Tapestries of Mathematics and Mysticism, Sterling, NY, 2009, page 33. LINKS MATHEMATICA tri[n_] := n (n + 1)/2; f[n_] := Block[{k = n + 1, t = tri@n}, While[ !IntegerQ@ Sqrt[ t*tri@k], k++ ]; k]; Table[ f@n, {n, 2, 46}] CROSSREFS Cf. A132596, A007654, A132584. Sequence in context: A141767 A183008 A054734 * A029613 A083541 A073763 Adjacent sequences:  A174903 A174904 A174905 * A174907 A174908 A174909 KEYWORD nonn AUTHOR Robert G. Wilson v, Apr 01 2010 STATUS approved

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