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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. 3
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 (list; table; graph; refs; listen; history; text; internal format)
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: A070871 A096115 A093919 * A178888 A068424 A139359

Adjacent sequences:  A179658 A179659 A179660 * A179662 A179663 A179664

KEYWORD

nonn,tabl

AUTHOR

Enrique Pérez Herrero, Jan 09 2011

STATUS

approved

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Last modified October 23 13:13 EDT 2014. Contains 248464 sequences.