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Triangle read by rows: T(n, k) = Product_{p in PF(n) symmetric difference PF(k)} p, where PF(a) is the set of the prime factors of a.
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%I #20 Jul 13 2024 10:12:41

%S 1,1,1,2,2,1,3,3,6,1,2,2,1,6,1,5,5,10,15,10,1,6,6,3,2,3,30,1,7,7,14,

%T 21,14,35,42,1,2,2,1,6,1,10,3,14,1,3,3,6,1,6,15,2,21,6,1,10,10,5,30,5,

%U 2,15,70,5,30,1,11,11,22,33,22,55,66,77,22,33,110,1

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

%F From _Michael De Vlieger_, Jul 11 2024: (Start)

%F T(0,0) = T(n,0) = rad(n)/rad(0) = 1 where rad = A007947;

%F T(n,k) = rad(k*n)/rad(gcd(k,n))

%F = A007947(k*n)/A007947(S(n,k)) where S = A050873

%F = A374436(n,k)/A374433(n,k). (End)

%e [ 0] 1;

%e [ 1] 1, 1;

%e [ 2] 2, 2, 1;

%e [ 3] 3, 3, 6, 1;

%e [ 4] 2, 2, 1, 6, 1;

%e [ 5] 5, 5, 10, 15, 10, 1;

%e [ 6] 6, 6, 3, 2, 3, 30, 1;

%e [ 7] 7, 7, 14, 21, 14, 35, 42, 1;

%e [ 8] 2, 2, 1, 6, 1, 10, 3, 14, 1;

%e [ 9] 3, 3, 6, 1, 6, 15, 2, 21, 6, 1;

%e [10] 10, 10, 5, 30, 5, 2, 15, 70, 5, 30, 1;

%e [11] 11, 11, 22, 33, 22, 55, 66, 77, 22, 33, 110, 1;

%p PF := n -> ifelse(n = 0, {}, NumberTheory:-PrimeFactors(n)):

%p A374434 := (n, k) -> mul(symmdiff(PF(n), PF(k))):

%p seq(print(seq(A374434(n, k), k = 0..n)), n = 0..11);

%t nn = 12; Do[Set[s[i], FactorInteger[i][[All, 1]]], {i, 0, nn}]; s[0] = {1}; Table[Times @@ SymmetricDifference[s[k], s[n]], {n, 0, nn}, {k, 0, n}] // Flatten (* _Michael De Vlieger_, Jul 11 2024 *)

%o (Python) # Function A374434 defined in A374433.

%o for n in range(11): print([A374434(n, k) for k in range(n + 1)])

%Y Family: A374433 (intersection), this sequence (symmetric difference), A374435 (difference), A374436 (union).

%Y Cf. A007947 (column 0), A000034 (central terms), A050873 (gcd).

%K nonn,tabl

%O 0,4

%A _Peter Luschny_, Jul 10 2024