A374436 - OEIS

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.

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

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

0,4

LINKS

Table of n, a(n) for n=0..77.

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

Adjacent sequences: A374433 A374434 A374435 * A374437 A374438 A374439

KEYWORD

nonn,tabl

AUTHOR

Peter Luschny, Jul 10 2024

STATUS

approved