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A374436 Triangle read by rows: T(n, k) = Product_{p in PF(n) union PF(k)} p, where PF(a) is the set of the prime factors of a.

%I A374436 #16 Jul 13 2024 10:12:54
%S A374436 1,1,1,2,2,2,3,3,6,3,2,2,2,6,2,5,5,10,15,10,5,6,6,6,6,6,30,6,7,7,14,
%T A374436 21,14,35,42,7,2,2,2,6,2,10,6,14,2,3,3,6,3,6,15,6,21,6,3,10,10,10,30,
%U A374436 10,10,30,70,10,30,10,11,11,22,33,22,55,66,77,22,33,110,11
%N A374436 Triangle read by rows: T(n, k) = Product_{p in PF(n) union PF(k)} p, where PF(a) is the set of the prime factors of a.
%F A374436 T(0,0) = T(n,0) = 1; T(n,k) = rad(k*n) where rad = A007947. - _Michael De Vlieger_, Jul 11 2024
%e A374436   [ 0]  1;
%e A374436   [ 1]  1,  1;
%e A374436   [ 2]  2,  2,  2;
%e A374436   [ 3]  3,  3,  6,  3;
%e A374436   [ 4]  2,  2,  2,  6,  2;
%e A374436   [ 5]  5,  5, 10, 15, 10,  5;
%e A374436   [ 6]  6,  6,  6,  6,  6, 30,  6;
%e A374436   [ 7]  7,  7, 14, 21, 14, 35, 42,  7;
%e A374436   [ 8]  2,  2,  2,  6,  2, 10,  6, 14,  2;
%e A374436   [ 9]  3,  3,  6,  3,  6, 15,  6, 21,  6,  3;
%e A374436   [10] 10, 10, 10, 30, 10, 10, 30, 70, 10, 30,  10;
%e A374436   [11] 11, 11, 22, 33, 22, 55, 66, 77, 22, 33, 110, 11;
%p A374436 PF := n -> ifelse(n = 0, {}, NumberTheory:-PrimeFactors(n)):
%p A374436 A374436 := (n, k) -> mul(PF(n) union PF(k)):
%p A374436 seq(print(seq(A374436(n, k), k = 0..n)), n = 0..11);
%t A374436 nn = 12; Do[Set[s[i], FactorInteger[i][[All, 1]]], {i, 0, nn}]; s[0] = {1}; Table[Apply[Times, Union[s[k], s[n]]], {n, 0, nn}, {k, 0, n}] // Flatten (* _Michael De Vlieger_, Jul 11 2024 *)
%o A374436 (Python)  # Function A374436 defined in A374433.
%o A374436 for n in range(12): print([A374436(n, k) for k in range(n + 1)])
%Y A374436 Family: A374433 (intersection), A374434 (symmetric difference), A374435 (difference), this sequence (union).
%Y A374436 Cf. A007947 (column 0, main diagonal), A099985 (central terms).
%K A374436 nonn,tabl
%O A374436 0,4
%A A374436 _Peter Luschny_, Jul 10 2024