A140819 Triangle read by rows: T(n, m) = m if 2*m = n, otherwise 2*gcd(n, m).

0, 2, 2, 4, 1, 4, 6, 2, 2, 6, 8, 2, 2, 2, 8, 10, 2, 2, 2, 2, 10, 12, 2, 4, 3, 4, 2, 12, 14, 2, 2, 2, 2, 2, 2, 14, 16, 2, 4, 2, 4, 2, 4, 2, 16, 18, 2, 2, 6, 2, 2, 6, 2, 2, 18

Offset: 0

Author

Roger L. Bagula and Mats Granvik, Jul 16 2008

Keywords

• nonn
• tabl

Examples

			{0},
{2, 2},
{4, 1, 4},
{6, 2, 2, 6},
{8, 2, 2, 2, 8},
{10, 2, 2, 2, 2, 10},
{12, 2, 4, 3, 4, 2, 12},
{14, 2, 2, 2, 2, 2, 2, 14},
{16, 2, 4, 2, 4, 2, 4, 2, 16},
{18, 2, 2, 6, 2, 2, 6, 2, 2, 18}
		

Crossrefs

Cf. A109004, A140685.

Programs

Mathematica

M[d_, x_, y_] := Sum[Sum[If[n == m, GCD[d - 1, m - 1], If[n == d - m + 1, GCD[ d - 1, n - 1], 0]]*x^(n - 1)*y^(m - 1), {n, 1, d}], {m, 1, d}]
Table[CoefficientList[M[d, x, 1], x], {d, 1, 10}]
Flatten[%]
Table[Apply[Plus, CoefficientList[M[d, x, 1], x]], {d, 1, 10}]

Extensions

Definition simplified by the editors of the OEIS, Jan 03 2024