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A374443
Triangle read by rows: T(n, k) = rad(gcd(n, k)) if n, k > 0, T(0, 0) = 1, where rad = A007947 and gcd = A109004.
1
1, 1, 1, 2, 1, 2, 3, 1, 1, 3, 2, 1, 2, 1, 2, 5, 1, 1, 1, 1, 5, 6, 1, 2, 3, 2, 1, 6, 7, 1, 1, 1, 1, 1, 1, 7, 2, 1, 2, 1, 2, 1, 2, 1, 2, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 10, 1, 2, 1, 2, 5, 2, 1, 2, 1, 10, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 6, 1, 2, 3, 2, 1, 6, 1, 2, 3, 2, 1, 6
OFFSET
0,4
EXAMPLE
Triangle starts:
[ 0] 1;
[ 1] 1, 1;
[ 2] 2, 1, 2;
[ 3] 3, 1, 1, 3;
[ 4] 2, 1, 2, 1, 2;
[ 5] 5, 1, 1, 1, 1, 5;
[ 6] 6, 1, 2, 3, 2, 1, 6;
[ 7] 7, 1, 1, 1, 1, 1, 1, 7;
[ 8] 2, 1, 2, 1, 2, 1, 2, 1, 2;
[ 9] 3, 1, 1, 3, 1, 1, 3, 1, 1, 3;
[10] 10, 1, 2, 1, 2, 5, 2, 1, 2, 1, 10;
[11] 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11;
MAPLE
rad := n -> ifelse(n = 0, 1, NumberTheory:-Radical(n)):
T := (n, k) -> rad(igcd(n, k)); seq(seq(T(n, k), k = 0..n), n = 0..11);
MATHEMATICA
rad[n_] := If[n == 0, 1, Product[p, {p, Select[Divisors[n], PrimeQ]}]];
T[n_, k_] := rad[GCD[n, k]]; Table[T[n, k], {n, 0, 10}, {k, 0, n}] // Flatten
CROSSREFS
Variant: A374433.
Cf. A374442 (row sums), A007947, A109004.
Sequence in context: A162319 A237594 A098666 * A362890 A306251 A364027
KEYWORD
nonn,tabl
AUTHOR
STATUS
approved