A098666 - OEIS

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

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OFFSET

1,3

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.

LINKS

Table of n, a(n) for n=1..105.

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<n.

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 *)

CROSSREFS

Sequence in context: A215026 A162319 A237594 * A374443 A362890 A306251

Adjacent sequences: A098663 A098664 A098665 * A098667 A098668 A098669

KEYWORD

nonn,tabl

AUTHOR

Reinhard Zumkeller, Sep 20 2004

STATUS

approved