A343004 - OEIS

%I #25 May 01 2021 22:14:44

%S 2,3,2,5,2,7,3,5,3,7,2,11,2,13,3,11,2,17,5,7,2,19,3,13,2,23,3,17,5,11,

%T 3,19,2,29,2,31,5,13,3,23,2,37,7,11,2,41,5,17,2,43,3,29,7,13,3,31,2,

%U 47,5,19,2,53,3,37,5,23,2,59,7,17,2,61,3,41,3,43,7,19,2,67,3,47,2,71,11,13,5,29

%N Pairwise listing of the prime factors of the squarefree semiprimes (smaller, larger).

%C Interspersion of A096916 and A070647.

%e The first squarefree semiprime is 6 = 2*3.  Therefore a(1) = 2 and a(2) = 3.

%t Flatten@ Map[FactorInteger[#][[All, 1]] &, Select[Range[6, 150], And[PrimeOmega[#] == 2, SquareFreeQ[#]] &]] (* or *)

%t Block[{nn = 35, a = {}, lim}, lim = Prime[nn]; Do[Do[If[#3 <= lim, AppendTo[a, {#3, #2, #1}], Break[]] & @@ {#1, #2, #1 #2} & @@ {Prime[i], Prime[j]}, {i, j + 1, nn}], {j, nn}]; Flatten@ Sort[a][[All, 2 ;; 3]]] (* _Michael De Vlieger_, May 01 2021 *)

%Y Cf. A006881, A096916 and A070647 (lesser and larger prime factors).

%K nonn

%O 1,1

%A _Wesley Ivan Hurt_, Apr 28 2021