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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.
4
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, 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, 10, 10, 30, 70, 10, 30, 10, 11, 11, 22, 33, 22, 55, 66, 77, 22, 33, 110, 11
OFFSET
0,4
FORMULA
T(0,0) = T(n,0) = 1; T(n,k) = rad(k*n) where rad = A007947. - Michael De Vlieger, Jul 11 2024
EXAMPLE
[ 0] 1;
[ 1] 1, 1;
[ 2] 2, 2, 2;
[ 3] 3, 3, 6, 3;
[ 4] 2, 2, 2, 6, 2;
[ 5] 5, 5, 10, 15, 10, 5;
[ 6] 6, 6, 6, 6, 6, 30, 6;
[ 7] 7, 7, 14, 21, 14, 35, 42, 7;
[ 8] 2, 2, 2, 6, 2, 10, 6, 14, 2;
[ 9] 3, 3, 6, 3, 6, 15, 6, 21, 6, 3;
[10] 10, 10, 10, 30, 10, 10, 30, 70, 10, 30, 10;
[11] 11, 11, 22, 33, 22, 55, 66, 77, 22, 33, 110, 11;
MAPLE
PF := n -> ifelse(n = 0, {}, NumberTheory:-PrimeFactors(n)):
A374436 := (n, k) -> mul(PF(n) union PF(k)):
seq(print(seq(A374436(n, k), k = 0..n)), n = 0..11);
MATHEMATICA
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 *)
PROG
(Python) # Function A374436 defined in A374433.
for n in range(12): print([A374436(n, k) for k in range(n + 1)])
CROSSREFS
Family: A374433 (intersection), A374434 (symmetric difference), A374435 (difference), this sequence (union).
Cf. A007947 (column 0, main diagonal), A099985 (central terms).
Sequence in context: A238220 A103600 A267160 * A082861 A131704 A327746
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, Jul 10 2024
STATUS
approved