A188663 Pentagonal numbers that are the product of two pentagonal numbers greater than 1.

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

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.

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: A213318 A346026 A097648 * A250711 A223431 A203089

Adjacent sequences: A188660 A188661 A188662 * A188664 A188665 A188666

Keyword

nonn

Author

T. D. Noe, Apr 07 2011

Status

approved