%I #47 Nov 25 2021 09:38:04

%S 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 22,26,23,57,31,61,21,32,25,30,36,67,29,40,35,74,41,81,39,42,45,89,46,

%U 50,34,47,48,100,49,53,38,56,52,107,60,115,51,64,54,59

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

%C This is a permutation of the positive integers.

%C 1, 2, 6, 9, 15, 19, ... are in a(n) and A064664(n).

%H Jean-François Alcover, <a href="/A347348/b347348.txt">Table of n, a(n) for n = 1..1000</a>

%H Jean-François Alcover, <a href="/A347348/a347348.pdf">Plot of a(1..1000)</a>

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

%F Interleave the occurrences in A164912.

%t nmax = 120;

%t 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 b[n_] := Quotient[ekg[n] - 1, 2] + 1;

%t bb = Array[b, nmax];

%t TakeWhile[Table[Position[bb, n], {n, 1, nmax}], Length[#] == 2&] // Flatten (* _Jean-François Alcover_, Nov 21 2021 *)

%Y Cf. A000027, A008619, A164912.

%Y Cf. A064664.

%K nonn

%O 1,2

%A _Paul Curtz_, Nov 21 2021