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

Author

T. D. Noe, Apr 07 2011

Keywords

• nonn

Comments

See A188630 for the triangular case and A188660 for the oblong case.

Examples

			11310 = 5 * 2262; that is, pen(87) = pen(2) * pen(39).
		

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.

Crossrefs

Cf. A000326 (pentagonal numbers).

Programs

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]]]