%I #10 Jun 07 2014 01:36:51
%S 1,3,5,2,7,9,11,4,6,13,15,8,17,19,21,10,23,12,25,14,27,29,31,16,18,33,
%T 20,22,35,37,39,24,41,43,45,26,47,49,51,28,53,55,57,30,32,59,61,34,36,
%U 38,63,40,65,42,67,44,69,71,73,46,75,77,48,50,79,81,83,52,85,87,89
%N If n is k-th squarefree number [i.e., n = A005117(k)], a(n) = 2k-1; otherwise, when n is k-th nonsquarefree number [i.e., n = A013929(k)], a(n) = 2k.
%C Odd numbers occur (in order) at the positions given by squarefree numbers, A005117, and even numbers occur (in order) at the positions given by their complement, nonsquarefree numbers, A013929.
%H Antti Karttunen, <a href="/A243352/b243352.txt">Table of n, a(n) for n = 1..10001</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F If mu(n) = 0, a(n) = 2*A057627(n), otherwise, a(n) = 1 + 2 * A013928(n). [Here mu is Moebius mu-function, A008683, which is zero only when n is a nonsquarefree number, one of the numbers in A013929].
%F For all n, A000035(a(n)) = A008966(n) = A008683(n)^2, or equally, a(n) = mu(n) modulo 2.
%o (Scheme) (define (A243352 n) (if (zero? (A008966 n)) (* 2 (A057627 n)) (+ (* 2 (A013928 n)) 1)))
%Y Inverse: A088610. Cf. A243343, A072062.
%K nonn,easy
%O 1,2
%A _Antti Karttunen_, Jun 04 2014