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A188660
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Oblong numbers that are the product of two oblong numbers.
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3
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12, 72, 240, 420, 600, 1260, 2352, 4032, 6480, 7140, 9900, 14280, 14520, 20592, 28392, 38220, 46872, 50400, 65280, 78120, 83232, 104652, 123552, 129960, 159600, 194040, 233772, 279312, 291060, 331200, 390000, 456300, 485112, 530712, 609180, 613872, 699732, 706440, 809100, 852852, 922560
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OFFSET
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1,1
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COMMENTS
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Breiteig writes about the finding these numbers, but does not list these numbers as a sequence. The problem can be extended to any polygonal number: for example, when is a pentagonal number the product of two pentagonal numbers? See A188630 and A188663 for the triangular and pentagonal cases.
As shown in the example, the product of consecutive oblong numbers is also oblong: oblong(n) * oblong(n+1) = oblong(n*(n+2)).
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LINKS
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Donovan Johnson, Table of n, a(n) for n = 1..5000
Trygve Breiteig, When is the product of two oblong numbers another oblong?, Math. Mag. 73 (2000), 120-129.
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EXAMPLE
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240 = 12 * 20; that is, oblong(15) = oblong(3) * oblong(4).
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MATHEMATICA
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OblongQ[n_] := IntegerQ[Sqrt[1 + 4 n]]; OblongIndex[n_] := Floor[(-1 + Sqrt[1 + 4*n])/2]; lim = 10^6; nMax = OblongIndex[lim/2]; obl = Table[n (n + 1), {n, nMax}]; Union[Reap[Do[num = obl[[i]]*obl[[j]]; If[OblongQ[num], Sow[num]], {i, OblongIndex[Sqrt[lim]]}, {j, i, OblongIndex[lim/obl[[i]]]}]][[2, 1]]]
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CROSSREFS
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Cf. A002378 (oblong numbers).
Sequence in context: A101523 A143698 A199531 * A047928 A008533 A010024
Adjacent sequences: A188657 A188658 A188659 * A188661 A188662 A188663
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KEYWORD
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nonn
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AUTHOR
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T. D. Noe, Apr 07 2011
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STATUS
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approved
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