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A098666 Triangle read by rows, 1<=k<=n: the n-th row contains the first n numbers after pairwise reducing all common divisors from left to right.

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%I A098666 #8 Sep 20 2021 05:17:14
%S A098666 1,1,2,1,2,3,1,1,3,2,1,1,3,2,5,1,1,1,1,5,1,1,1,1,1,5,1,7,1,1,1,1,5,1,
%T A098666 7,8,1,1,1,1,5,1,7,8,9,1,1,1,1,1,1,7,4,9,1,1,1,1,1,1,1,7,4,9,1,11,1,1,
%U A098666 1,1,1,1,7,1,3,1,11,1,1,1,1,1,1,1,7,1,3,1,11,1,13,1,1,1,1,1,1,1,1,3,1,11,1,13,2
%N A098666 Triangle read by rows, 1<=k<=n: the n-th row contains the first n numbers after pairwise reducing all common divisors from left to right.
%C A098666 A098667(n) = Max{m: T(n,k)=1 for 1<=k<=m<=n};
%C A098666 A098668(n) = T(n,n);
%C A098666 T(A098669(n), A098669(n)) = 1;
%C A098666 A008339 gives row-products.
%F A098666 T(n, n)=X(n, n-1) and T(n, k)=T(n-1, k)/GCD(T(n-1, k), X(n, k-1)), where X(n, 0)=n and X(n, k)=X(n, k-1)/GCD(T(n-1, k), X(n, k-1)) for 1<=k<n.
%t A098666 T[n_, n_] := X[n, n-1];
%t A098666 T[n_, k_] := T[n, k] = T[n-1, k]/GCD[T[n-1, k], X[n, k-1]];
%t A098666 X[n_, 0] := n;
%t A098666 X[n_, k_] := X[n, k] = X[n, k-1]/GCD[T[n-1, k], X[n, k-1]];
%t A098666 Table[T[n, k], {n, 1, 14}, {k, 1, n}] // Flatten (* _Jean-François Alcover_, Sep 20 2021 *)
%K A098666 nonn,tabl
%O A098666 1,3
%A A098666 _Reinhard Zumkeller_, Sep 20 2004