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

1,2

Comments

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

Main diagonal is A003418.

Links

Table of n, a(n) for n=1..58.

Formula

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

Example

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

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]]

Prog

(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

Crossrefs

Cf. A093919, A096179, A003418.

Sequence in context: A289838 A290734 A093919 * A178888 A068424 A298484

Adjacent sequences: A179658 A179659 A179660 * A179662 A179663 A179664

Keyword

nonn,tabl

Author

Enrique Pérez Herrero, Jan 09 2011

Status

approved