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A188663
Pentagonal numbers that are the product of two pentagonal numbers greater than 1.
5
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
OFFSET
1,1
COMMENTS
See A188630 for the triangular case and A188660 for the oblong case.
LINKS
Trygve Breiteig, When is the product of two oblong numbers another oblong?, Math. Mag. 73 (2000), 120-129.
EXAMPLE
11310 = 5 * 2262; that is, pen(87) = pen(2) * pen(39).
MATHEMATICA
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]]]
CROSSREFS
Cf. A000326 (pentagonal numbers).
Sequence in context: A346026 A097648 A374372 * A250711 A223431 A203089
KEYWORD
nonn
AUTHOR
T. D. Noe, Apr 07 2011
STATUS
approved