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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.
4
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
1,3
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.
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
KEYWORD
nonn,tabl
AUTHOR
_Reinhard Zumkeller_, Sep 20 2004
STATUS
approved