A343004 Pairwise listing of the prime factors of the squarefree semiprimes (smaller, larger).
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, 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, 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
Offset: 1
Keywords
Examples
The first squarefree semiprime is 6 = 2*3. Therefore a(1) = 2 and a(2) = 3.
Programs
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Mathematica
Flatten@ Map[FactorInteger[#][[All, 1]] &, Select[Range[6, 150], And[PrimeOmega[#] == 2, SquareFreeQ[#]] &]] (* or *) 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 *)
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