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A347348 a(n) is the rank of A008619(n) in A164912.

%I A347348 #47 Nov 25 2021 09:38:04
%S A347348 1,2,3,5,4,10,8,14,6,9,7,20,13,28,11,17,12,33,18,37,15,19,16,43,24,27,
%T A347348 22,26,23,57,31,61,21,32,25,30,36,67,29,40,35,74,41,81,39,42,45,89,46,
%U A347348 50,34,47,48,100,49,53,38,56,52,107,60,115,51,64,54,59
%N A347348 a(n) is the rank of A008619(n) in A164912.
%C A347348 This is a permutation of the positive integers.
%C A347348 1, 2, 6, 9, 15, 19, ... are in a(n) and A064664(n).
%H A347348 Jean-François Alcover, <a href="/A347348/b347348.txt">Table of n, a(n) for n = 1..1000</a>
%H A347348 Jean-François Alcover, <a href="/A347348/a347348.pdf">Plot of a(1..1000)</a>
%H A347348 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A347348 Interleave the occurrences in A164912.
%t A347348 nmax = 120;
%t A347348 ekg[n_] := ekg[n] = Module[{ee, k}, If[n <= 2, n, ee = Array[ekg, n - 1]; For[k = 1, True, k++, If[FreeQ[ee, k] && GCD[ekg[n - 1], k] != 1, Return[k]]]]];
%t A347348 b[n_] := Quotient[ekg[n] - 1, 2] + 1;
%t A347348 bb = Array[b, nmax];
%t A347348 TakeWhile[Table[Position[bb, n], {n, 1, nmax}], Length[#] == 2&] // Flatten (* _Jean-François Alcover_, Nov 21 2021 *)
%Y A347348 Cf. A000027, A008619, A164912.
%Y A347348 Cf. A064664.
%K A347348 nonn
%O A347348 1,2
%A A347348 _Paul Curtz_, Nov 21 2021