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A188663
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Pentagonal numbers that are the product of two pentagonal numbers greater than 1.
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4
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10045, 11310, 52360, 230300, 341055, 4048352, 6192520, 16008300, 18573282, 21430710, 44175780, 49452975, 75377337, 89579112, 174695500, 201243042, 212087876, 616116800, 755319180, 1369585525, 1557466482, 1586309340, 1625178126, 1674425676, 1744607172, 1857169860, 1868270250, 1985347551
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OFFSET
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1,1
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COMMENTS
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See A188630 for the triangular case and A188660 for the oblong case.
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LINKS
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Donovan Johnson, Table of n, a(n) for n = 1..361
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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11310 = 5 * 2262; that is, pen(87) = pen(2) * pen(39).
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MATHEMATICA
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PentagonalQ[n_] := IntegerQ[(1 + Sqrt[1 + 24*n])/6]; PenIndex[n_] := Floor[(1 + Sqrt[1 + 24*n])/6]; lim = 10^10; nMax = PenIndex[lim/5]; pen = Table[n (3 n - 1)/2, {n, 2, nMax}]; Union[Reap[Do[num = pen[[i]]*pen[[j]]; If[PentagonalQ[num], Sow[num]], {i, PenIndex[Sqrt[lim]]}, {j, i, PenIndex[lim/pen[[i]]] - 1}]][[2, 1]]]
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CROSSREFS
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Cf. A000326 (pentagonal numbers).
Sequence in context: A213318 A346026 A097648 * A250711 A223431 A203089
Adjacent sequences: A188660 A188661 A188662 * A188664 A188665 A188666
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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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