A179661 Triangle read by rows: T(n,k) is the largest least common multiple of any k-element subset of the first n positive integers.

1, 2, 2, 3, 6, 6, 4, 12, 12, 12, 5, 20, 60, 60, 60, 6, 30, 60, 60, 60, 60, 7, 42, 210, 420, 420, 420, 420, 8, 56, 280, 840, 840, 840, 840, 840, 9, 72, 504, 2520, 2520, 2520, 2520, 2520, 2520, 10, 90, 630, 2520, 2520, 2520, 2520, 2520, 2520, 2520, 11, 110, 990

Offset: 1

Author

Enrique Pérez Herrero, Jan 09 2011

Keywords

• nonn
• tabl

Comments

Sequence differs from A093919; first divergences are at indices 31, 40, 48, 59.

Main diagonal is A003418.

Examples

			Triangle begins:
    [ 1 ],
    [ 2, 2 ],
    [ 3, 6, 6 ],
    [ 4, 12, 12, 12 ],
    [ 5, 20, 60, 60, 60 ],
    [ 6, 30, 60, 60, 60, 60 ].
		

Crossrefs

Cf. A093919, A096179, A003418.

Programs

Magma

A179661:=func< n, k | Max([ LCM(s): s in Subsets({1..n}, k) ]) >; z:=12; [ A179661(n, k): k in [1..n], n in [1..z] ]; // Klaus Brockhaus, Jan 16 2011

Mathematica

A179661[n_,k_]:=Max[LCM@@@Subsets[Range[n],{k}]];
A002260[n_]:=n-Binomial[Floor[1/2+Sqrt[2*n]],2];
A002024[n_]:=Floor[1/2+Sqrt[2*n]];
A179661[n_]:=A179661[A002024[n],A002260[n]]

Formula

T(n,k) = max{ lcm(x_1,...,x_k) ; 0 < x_1 < ... < x_k <= n }.