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

1,1

Comments

Interspersion of A096916 and A070647.

Links

Table of n, a(n) for n=1..88.

Example

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

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 *)

Crossrefs

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

Sequence in context: A280503 A094757 A095171 * A270443 A096776 A347043

Adjacent sequences: A343001 A343002 A343003 * A343005 A343006 A343007

Keyword

nonn

Author

Wesley Ivan Hurt, Apr 28 2021

Status

approved