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
Programs
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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
A098669 Numbers of rows ending with ones in triangle A098666.
1, 6, 10, 12, 20, 26, 30, 34, 38, 46, 52, 58, 60, 66, 68, 74, 78, 82, 86, 92, 102, 105, 106, 114, 116, 122, 130, 134, 136, 142, 146, 148, 156, 164, 165, 166, 172, 178, 186, 190, 194, 202, 206, 212, 218, 222, 226, 228, 230, 238, 244, 246, 252, 262, 264, 273, 274
Offset: 1
Keywords
Comments
A098668(a(n)) = 1;
a(22)=105 is the smallest odd term, 105=3*5*7.
Comments