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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.

%I A179661 #16 Sep 08 2022 08:45:54
%S A179661 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,
%T A179661 420,420,420,8,56,280,840,840,840,840,840,9,72,504,2520,2520,2520,
%U A179661 2520,2520,2520,10,90,630,2520,2520,2520,2520,2520,2520,2520,11,110,990
%N 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.
%C A179661 Sequence differs from A093919; first divergences are at indices 31, 40, 48, 59.
%C A179661 Main diagonal is A003418.
%F A179661 T(n,k) = max{ lcm(x_1,...,x_k) ; 0 < x_1 < ... < x_k <= n }.
%e A179661 Triangle begins:
%e A179661     [ 1 ],
%e A179661     [ 2, 2 ],
%e A179661     [ 3, 6, 6 ],
%e A179661     [ 4, 12, 12, 12 ],
%e A179661     [ 5, 20, 60, 60, 60 ],
%e A179661     [ 6, 30, 60, 60, 60, 60 ].
%t A179661 A179661[n_,k_]:=Max[LCM@@@Subsets[Range[n],{k}]];
%t A179661 A002260[n_]:=n-Binomial[Floor[1/2+Sqrt[2*n]],2];
%t A179661 A002024[n_]:=Floor[1/2+Sqrt[2*n]];
%t A179661 A179661[n_]:=A179661[A002024[n],A002260[n]]
%o A179661 (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
%Y A179661 Cf. A093919, A096179, A003418.
%K A179661 nonn,tabl
%O A179661 1,2
%A A179661 _Enrique Pérez Herrero_, Jan 09 2011