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%I #9 Aug 11 2014 22:45:46
%S 10045,11310,52360,230300,341055,4048352,6192520,16008300,18573282,
%T 21430710,44175780,49452975,75377337,89579112,174695500,201243042,
%U 212087876,616116800,755319180,1369585525,1557466482,1586309340,1625178126,1674425676,1744607172,1857169860,1868270250,1985347551
%N Pentagonal numbers that are the product of two pentagonal numbers greater than 1.
%C See A188630 for the triangular case and A188660 for the oblong case.
%H Donovan Johnson, <a href="/A188663/b188663.txt">Table of n, a(n) for n = 1..361</a>
%H Trygve Breiteig, <a href="http://www.jstor.org/pss/2691083">When is the product of two oblong numbers another oblong?</a>, Math. Mag. 73 (2000), 120-129.
%e 11310 = 5 * 2262; that is, pen(87) = pen(2) * pen(39).
%t 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]]]
%Y Cf. A000326 (pentagonal numbers).
%K nonn
%O 1,1
%A _T. D. Noe_, Apr 07 2011
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