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.

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, 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, 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

Offset: 1

Author

Reinhard Zumkeller, Sep 20 2004

Keywords

• nonn
• tabl

Comments

A098667(n) = Max{m: T(n,k)=1 for 1<=k<=m<=n};

A098668(n) = T(n,n);

T(A098669(n), A098669(n)) = 1;

A008339 gives row-products.

Programs

Mathematica

T[n_, n_] := X[n, n-1];
T[n_, k_] := T[n, k] = T[n-1, k]/GCD[T[n-1, k], X[n, k-1]];
X[n_, 0] := n;
X[n_, k_] := X[n, k] = X[n, k-1]/GCD[T[n-1, k], X[n, k-1]];
Table[T[n, k], {n, 1, 14}, {k, 1, n}] // Flatten (* Jean-François Alcover, Sep 20 2021 *)

Formula

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

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