Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #17 Jun 08 2014 08:57:03
%S 1,4,8,2,9,12,16,3,5,18,20,6,24,25,27,7,28,10,32,11,36,40,44,13,14,45,
%T 15,17,48,49,50,19,52,54,56,21,60,63,64,22,68,72,75,23,26,76,80,29,30,
%U 31,81,33,84,34,88,35,90,92,96,37,98,99,38,39,100,104,108,41,112,116
%N a(1) = 1, a(n) is the smallest squarefree number not included earlier if n is not squarefree, else n is the smallest nonsquarefree number.
%C From _Antti Karttunen_, Jun 04 2014: (Start)
%C This is a self-inverse permutation (involution) of natural numbers.
%C After 1, nonsquarefree numbers occur (in monotonic order) at the positions given by squarefree numbers, A005117, and squarefree numbers occur (in monotonic order) at the positions given by their complement, nonsquarefree numbers, A013929.
%C (End)
%H Antti Karttunen, <a href="/A088609/b088609.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 From _Antti Karttunen_, Jun 04 2014: (Start)
%F a(1), and for n>1, if mu(n) = 0, a(n) = A005117(1+A057627(n)), otherwise, a(n) = A013929(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 > 1, A008966(a(n)) = 1 - A008966(n), or equally, mu(a(n)) + 1 = mu(n) modulo 2. [A property shared with A243347].
%F (End)
%o (define (A088609 n) (cond ((<= n 1) n) ((zero? (A008966 n)) (A005117 (+ 1 (A057627 n)))) (else (A013929 (A013928 n))))) ;; _Antti Karttunen_, Jun 04 2014
%Y Cf. A026239, A088610-A243352, A243347.
%K nonn
%O 1,2
%A _Amarnath Murthy_, Oct 16 2003
%E More terms from _Ray Chandler_, Oct 18 2003