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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.

%I A374443 #10 Jun 22 2025 02:57:40
%S A374443 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,
%T A374443 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,
%U A374443 1,1,1,1,1,1,1,1,1,1,11,6,1,2,3,2,1,6,1,2,3,2,1,6
%N 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.
%e A374443 Triangle starts:
%e A374443   [ 0]  1;
%e A374443   [ 1]  1, 1;
%e A374443   [ 2]  2, 1, 2;
%e A374443   [ 3]  3, 1, 1, 3;
%e A374443   [ 4]  2, 1, 2, 1, 2;
%e A374443   [ 5]  5, 1, 1, 1, 1, 5;
%e A374443   [ 6]  6, 1, 2, 3, 2, 1, 6;
%e A374443   [ 7]  7, 1, 1, 1, 1, 1, 1, 7;
%e A374443   [ 8]  2, 1, 2, 1, 2, 1, 2, 1, 2;
%e A374443   [ 9]  3, 1, 1, 3, 1, 1, 3, 1, 1, 3;
%e A374443   [10] 10, 1, 2, 1, 2, 5, 2, 1, 2, 1, 10;
%e A374443   [11] 11, 1, 1, 1, 1, 1, 1, 1, 1, 1,  1, 11;
%p A374443 rad := n -> ifelse(n = 0, 1, NumberTheory:-Radical(n)):
%p A374443 T := (n, k) -> rad(igcd(n, k)); seq(seq(T(n, k), k = 0..n), n = 0..11);
%t A374443 rad[n_] := If[n == 0, 1, Product[p, {p, Select[Divisors[n], PrimeQ]}]];
%t A374443 T[n_, k_] := rad[GCD[n, k]]; Table[T[n, k], {n, 0, 10}, {k, 0, n}] // Flatten
%o A374443 (Python)
%o A374443 from math import gcd, prod
%o A374443 from sympy.ntheory import primefactors
%o A374443 def T(n, k) -> int: return prod(primefactors(gcd(n, k)))
%o A374443 for n in range(16): print([T(n, k) for k in range(n+1)])  # _Peter Luschny_, Jun 22 2025
%Y A374443 Variant: A374433.
%Y A374443 Cf. A374442 (row sums), A007947, A109004.
%K A374443 nonn,tabl
%O A374443 0,4
%A A374443 _Peter Luschny_ and _Michael De Vlieger_, Jul 12 2024